graphing lines and writing equations of...

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Graphing Lines and

Writing Equations of

Lines

Name_____________________________

Math Teacher______________________________

http://www.google.com/url?sa=i&rct=j&q=slope+math&source=images&cd=&cad=rja&docid=j-xma23S4TZkYM&tbnid=6jkdfgw_YCiaUM:&ved=0CAUQjRw&url=http://www.howe-two.com/about/presentation/nctm.html&ei=lyRfUf6lJ4WXiAKW9YCQDQ&bvm=bv.44770516,d.cGE&psig=AFQjCNHD4O1te3OU06im4woW10eYGln2Jw&ust=1365276176079491

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Warm Ups

Date:

List the domain and range of each graph below.

a.

b.

c.

Date:

List the domain and range of each graph below. If there is a maximum or a minimum list that as well.

a.

b.

c.

Date:

List the domain:

List the range:

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Date:

List the domain and range

Date: List all intervals where the graphs are increasing and decreasing.

a. b. c.

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Date:

For the graph above:

Identify the domain and range.

Identify the minimum and maximum.

Identify the intervals where the graph increases and decreases

Date:

Use the mapping diagram above to answer the following:

Is it a function? What is the domain and range?

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Date: For each graph given provide a description of the function. Be sure to consider the following:

decreasing/increasing, min/max, domain/range, etc.

Date: For each graph given provide a description of the function. Be sure to consider the following:

decreasing/increasing, min/max, domain/range, etc.

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Linear Function: The Line

Formulas Slope: Slope-Intercept Form: Standard Form: Point-Slope Form:

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Linear Equations Overall Problem

John has $30 in his bank account. He plans on saving $5.25 per

week.

Part I

Write an equation for how much money, y, John will have after x weeks.

Part II

Graph the linear equation from above.

Part III

After 8 weeks how much money will John have saved?

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Plotting Points Notes

In order to plot a point you

must always start at the

origin. The origin is the point

(0,0)

All points on a graph are in

the form (x, y)

The x axis is the horizontal

axis on a graph.

With your pencil, darken the x

axis.

The y axis is the vertical axis

on a graph.

With your pencil, darken the y

axis.

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Steps to plot a point:

1. Start at the origin, which is the point (0,0)

2. Move to the right if your x coordinate is positive. Move to the left if your x-coordinate is negative.

3. After you have made it to the correct x coordinate, move up if your y coordinate is positive, move down if your y coordinate is negative.

Example:

Plot the point (0,- 4)

Example:

Plot the point (2, 3)

Example:

Plot the point (-2, -3)

Example:

Plot the point (-2, 3)

Example:

Plot the point (2,- 3)

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4.1 Check for Understanding

Sugar Prices

1. Which point shows the heaviest bag?

2. Which point shows the cheapest bag?

3. Which points show bags with the same weight?

4. Which points show bags with the same price?

5. Which of F or C gives the best value for money?

How can you tell?

Copyright © 2011 by Mathematics Assessment Sugar Prices

Each point on this graph represents a bag of sugar.

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Plotting points writing assignment

1. The horizontal axis is the ____-axis and the vertical axis is the ____-

axis.

2. The axes intersect at the ______________________ and divide the

coordinate plane into four sections called _____________________.

3. An ______________ _______________ identifies the location

of a point. The first number in an ordered pairs is called the ____-

coordinate and the second is called the ____-coordinate.

Free Response:

4. Your group member was absent on the day I taught how to graph points on

the coordinate plane. Explain to your friend how to plot the point (2, -5).

5. Explain to a friend the differences between graphing (0, 3) and (3, 0).

Identify the axis where each point will be located.

Word Bank: Use these words to fill in the blanks.

y, ordered pair, x, origin, y, quadrants, x

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Relations and Functions and Review of Domain and Range Notes

Relation

Review Domain

Review of Range

You Try

State the domain and range of the function

Example 2

Is the relation a function?

{(3, –2), (5, –1), (4, 0), (3, 1)}

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Example 3

State the domain and range


You Try

State the domain and range.


{(8, 2), (–4, 1), (–6, 2),(1, 9)}

You Try



Vertical Line Test

EXAMPLE



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You Try



You Try



You Try



You Try



You Try



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Classifying Relations as Functions

Relation Yes it is a Function

Explain Why

No it is not a Function

Explain Why Not

{(1,3) (1,4) (3, 5) (3,8)}

{(1, 3) (2, 4) (3, 5) (6, 8) }

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Ready Topic: Determine domain and range, and whether a relation is a function or not a function.

Determine if each set of ordered pairs is a function or not then state the domain and range.

1. { (-7, 2), (3, 5), (8, 4), (-6, 5), (-2, 3)} Function: Yes / No

Domain : Range:

2. { (9, 2), (0, 4), (4, 0), (5, 3), (2, 7) (0, -3), (3, -

1)}

Function: Yes / No

Domain : Range:

3. { (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 9)} Function: Yes / No

Domain : Range:

For the representation of the function given determine the domain and range.

Domain: Domain:

Range: Range: Is it a function? Is it a Function?

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Discrete: Items that can be counted

Continuous: Items that can be measured

For each topic below, decide if it is continuous or discrete. Justify your answer.

Topic Discrete Continuous Reason

Number of leaves on a

tree

The stars in the sky

The distance from

here to the moon

A bag of apples

Applesauce

A dozen eggs

Pearls on a necklace

Volume of a sphere

Chapters in a book

Buying tickets to a

concert

Buying deli meat by

the pound

Filling a bathtub with

water

The height of our

classmate

Number of books on a

shelf

Weight of a

watermelon

The age of a person

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Discrete and Continuous Domains-Notes

Discrete A discrete domain is a set of input values that

consists of only certain numbers in an interval.

Discrete data does not have meaning between the

data points.

You do not connect the points when the data is

discrete

Continuous A continuous domain is a set of input values that

consists of all numbers in an interval.

There is meaning between the points you plotted.

You connect the point when the data is continuous.

Ex 1: Are the data shown in the table discrete

or continuous? Explain.

Is the data discrete or continuous? Explain.

Ex: 2: The function y = 15.95x represents the

cost y (in dollars) of x tickets for the South

Florida Museum.


You Try:


You Try:


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Discrete and Continuous Domains-Practice

shirts Cost

1 $25

2 $50

3 $75

4 $100

5 $125

Josie bought DVDs for $15 each. She could

spend $60.

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State the domain and range for each graph and then tell if the graph is a function (write yes or no).

If the graph is a function, state whether it is discrete, continuous or neither.

1) Domain 2) Domain 3) Domain

Range Range Range

Function? Function? Function?


Range Range Range



Range Range Range


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Given the representation of the function(s) provided determine the domain, range, and whether the function is discrete, continuous, increasing, decreasing, etc.

Topic: Determine the following for each function: domain, range, discrete,

continuous, increasing, decreasing, etc.

9.

Description of Function:

Description of function: Description of function:

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Introduction: Exploring x & y-intercepts

Katarina’s family is traveling from Brownsville,

Texas, to their home in Laredo, Texas. The distance

from Brownsville to Laredo is 200 miles, and

Katarina’s mother is driving at a speed of 50 miles per

hour.

1. Complete the graph:

2. Graph

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3. What is the starting distance? What point on the graph corresponds to the starting distance? Where is this point located?

4. How long does it take to reach Laredo? What point on the graph corresponds to this time? Where is this point located?

5. Describe what it means for a point to lie on the y-axis in a graph of distance versus time.

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Graphing with x and y intercepts NOTES

Standard Form

x-intercept

y-intercept

The x-intercept of the graph is ( , )

The y-intercept of the graph is ( , )



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You Try! Find the x- and y-intercepts.



You Try!





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Step 1 Find the intercepts.


The y-intercept of the graph is ( , ) Step 2: Graph the intercepts:

Step 1 Find the intercepts.


The y-intercept of the graph is ( , ) Step 2: Graph the intercepts:

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Example 5:

The Lopez family lives 400 miles

from Denver. They drive to

Denver at a constant speed of

50mi/h. The function

xxf 50400)( gives their distance

in miles from Denver after x

hours.

A. Graph this function using

the intercepts.

B. What does each intercept

represent?

You Try:

An amateur filmmaker has

$6000 to make a film that

costs $75/h to produce. The

function f(x) = 6000 – 75x

gives the amount of money

left to make the film after x

hours of production. Graph

this function using the

intercepts. What does each

intercept represent?

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Intercepts - Problem Solving Notes/Guided Practice

1. You have $2.30 in dimes and nickels. The situation is given by 30.205.010.0 nd where d is the number of

dimes and n is the number of nickels. Find the x & y-intercept and explain their meaning in the context of

the problem.

2. You earn 80 points on a test that has questions worth 4 points and questions worth 5 points. The situation is

given by 8054 yx where x is the number of 4 point questions answered correctly and y is the number of 5

point questions answered correctly. Find the x & y-intercept and explain their meaning in the context of the

problem.

3. In one month you earn $240 babysitting for $10 per hour and dog walking for $8 per hour. The situation is

given by 240810 db where b is the number of hours you spend babysitting and d is the number of hours you

spend dog walking. Find the x & y-intercept and explain their meaning in the context of the problem.

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4. In one state, small bottles have a refund value of $.04 each, and large bottles have a refund value of $.08

each. Your friend returns both small and large bottles and receives $.56. This situation is given by

5684 yx where x is the number of small bottles and y is the number of large bottles.

a. Find the intercepts of the graph of the equation

b. Graph the equation.

c. Give three possibilities for the number of each size bottle your friend could have returned.

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5. Before 1979, there was no 3-point shot in professional basketball; players could score only 2-point field goals

and 1-point free throws. In a game before 1979, suppose a team scored a total of 128 points. This situation is

given by the equation 1282 yx where x is the possible number of field goals and y is the possible number of

free throws.

a. Find the intercepts of the graph of the equation.

b. Graph the equation.

c. What do the intercepts mean in this situation?

d. What are three possible numbers of field goals and free throws the team could have scored?

e. If the team made 24 free throws, how many field goals did it make?

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6. You borrow $180 from a friend who doesn’t charge you interest. You work out a payment schedule in which

you will make weekly payments to your friend. The balance B (in dollars) of the loan is given by the function

pnB 180 where p is the weekly payment and n is the number of weeks you make payments.

a. Without finding the intercepts state what they represent.

b. Graph the function if you make weekly payments of $20.

c. How long will it take to pay back your friend?

CHALLENGE Suppose you make payments of $20 for three weeks. Then you make payments of $15 until you

have paid your friend back. How does this affect the graph? How many payments do you make?

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Intercept Concept Task #1

The school store sells pens for $2.00 and notebooks for $3.00. The

equation 2x + 3y = 60 describes the number of pens x and notebooks y

that you can buy for $60.

1. Find the x and y intercepts and then graph the equation by plotting those two points.

(Be sure to mark your graph using an appropriate scale)

2. What does each intercept represent?

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Intercept Concept Task # 2

Kristyn rode a stationary bike at the gym. She programmed the timer for 20

minutes. The display counted backward to show how much time remained in her

workout. It also showed her mileage.

Time Remaining (in minutes) Distance Covered (in miles)

20 0

16 0.35

12 0.70

8 1.05

4 1.40

0 1.75

1. What are the x and y intercepts?

2. What do the intercepts represent?

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INTRO TO SLOPE: STEEPNESS OF A LINE

Below is a graph of 4 students driving to school 10 miles away.

1) Based on the graph below, predict the order in which they will arrive to school.

1st:

2nd:

3rd:

4th:

2) Do all students make it to school? Explain why or why not.

3) Give a possible explanation of what happened to Johnny.

4) How fast is Tom driving to school?

5) How fast is Mary driving to school?

6) How fast is Lucile driving to school?

Tom Mary Lucile

Johnn

y

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INTRO TO STORY GRAPHS

Directions:

1) Annotate this graph (using words such as increasing, decreasing, positive, negative, zero, quickly,

slowly,)

2) Label each point on then graph with the correct ordered pair.

3) Read the story that goes along with the graph. Is the story a good description of the graph?

My Dog Rough

My dog only weighed 3 pounds when he was born so I named him Rough because I thought he would

have a rough go at life. Rough’s first couple years matched his name as he only managed to gain a pound

during those first 2 years. Rough did much better over the next few years so that by the time he was 5 years

old he had doubled his weight from the 2 year mark. The next year we spent a lot of time outside playing and

running and he managed to lose a pound. The next year I made sure he ate healthier and Rough managed to

gain back that pound he had lost the year before. Eight pounds was the most Rough ever weighed because

during his 7th

year he began to steadily lose weight and only weighed 6 pounds when he died at age 10.

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Story Graphs

The sentences below describe the motion of five cars on a highway.

Match each sentence with the graph that represents it best.

1. The car’s speed remains constant.

Matching Graph ______

2. The car’s speed increases slowly but steadily.


3. The car’s speed increases sharply.


4. The car’s speed decreases gradually.


5. The car’s speed decreases suddenly.


6. Describe what it means for the graph of the car’s speed to be a horizontal line?

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Slope: Triangle Method NOTES (finding the rate of change using the

triangle method)

Slope

Rate of Change

The __________ or ______________________________ is the

difference in the y-values of ________ points on a line. The

__________ is the difference in the x-values of two points on a

____________. The slope of a line (m) is the _________ of rise

to run for any two points on the line.

Word Bank: slope, rate of change, ratio, run, rise, two

Positive Slope

Positive Rate of

Change

Negative Slope

Negative Rate of

Change

Picking two points on

the line.

Example 1:

Determine the rate of change of the

line:

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Example 2:

Determine the slope of the line:

Example 3:

Determine the rate of change of the

line:

Your Turn: Determine the clope of the below

`

Rate of Change of Straight Lines

Horizontal Lines

Vertical Lines

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You Try!!

What do you notice about the coordinates of the vertical line (a)?

What do you notice about the coordinates of the horizontal line (b)?

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Summary:

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Slope Triangle Method – Word Problems NOTES

1. The graph below shows the water leaking from a

pipe. Identify the slope and describe the meaning

in this situation.

4. The graph shows the cost for renting a bike.

Identify the slope and describe the meaning in this

situation.

2. The graph shows the cost for purchasing disks.

Identify the rate of change and describe the

meaning in this situation.

What is the cost of 1 disk? ______________

5. The graph shows the temperatures of an oven at

different times. Find the rate of change. Then tell

what it represents.

3. The graph to the right shows a hot air balloon

moving at a constant rate in the air. Identify the

rate of change and describe the meaning in this

situation.

.

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Slopes in the Real World

What is the slope?

What is the meaning of the slope?

What is the y intercept?

What does the y intercept represent?

What is the slope?




What is the slope?




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http://www.google.com/url?sa=i&rct=j&q=linear graphs of real life situations&source=images&cd=&cad=rja&docid=PvADI6FWlwsKjM&tbnid=BBpU1cfmjlIYeM:&ved=0CAUQjRw&url=http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/graphsrev6.shtml&ei=tHAuUoDTGqGK2gWj1IGICw&bvm=bv.51773540,d.aWc&psig=AFQjCNGqMkEVB1JoCgxUpnX2Hlh5_WFNLw&ust=1378861615658633

http://www.google.com/url?sa=i&rct=j&q=linear graphs of real life situations&source=images&cd=&cad=rja&docid=efv4oszvUjsejM&tbnid=Tz-kAArCmNd4KM:&ved=0CAUQjRw&url=http://www.projectsharetexas.org/resource/determine-meaning-slope-and-intercepts-real-world-example&ei=EXEuUvWcOYGN2gXl2YHwDQ&bvm=bv.51773540,d.b2I&psig=AFQjCNF1WDhZ1UPo1EHqvkkYMANHRLg7Mw&ust=1378861711478687

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Journey to the Bus Stop

Every morning Tom walks along a straight road from his home to a bus stop, a distance of 160 meters.

The graph shows his journey on one particular day.

1. Describe what may have happened.

You should include details like how fast he walked.

2. Are all sections of the graph realistic? Fully explain your answer

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Look at the Card Set Graphs and the Interpretations. Place the letter of the appropriate Graph

and Interpretation in the organizer.

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Relating Graphs to Stories-Interpreting Distance Time Graph Story Table

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Slope (Rate of Change) Formula Notes

Coordinates

Slope Formula

Example 1:

Find the slope of the line

that contains (2, 5) and (8,

1).

Example 2:

Find the rate of change the

line that contains

(–2, –2) and (7, –2).

You Try: 1

Find the slope of the line

that contains (5, –7) and

(6, –4).

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You Try: 2

Find the rate of change of

the line that contains

(5, 3)  and (–1, 4).

Example 3:

The graph shows the

average electricity costs in

dollars for operating a

refrigerator for several

months. Find the rate of

change of the line, and then

tell what the slope

represents.

You try 3


the line. What does it

represent in the context of

this situation?

You try 4


the line. What does it

represent in the context of

this situation?

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Rate of Change Word Problems– Slope from graphs and tables

Write your sentences on this side Show your calculations on this side!!!!

FUNDRAISING The table shows the amount of

money a Booster Club made washing cars for a

fundraiser. Use the information to find the rate of

change. Explain what the slope represents.

PLANES The table shows the number of miles a

plane traveled while in flight. Use the

information to find the approximate rate of

change in miles per minute. Explain what the

rate of change represents.

DRIVING The graph represents the distance

traveled while driving on a highway. Use the

graph to find the rate of change in miles per

hour. Explain what the slope represents.

DRIVING Use the graph to find the rate of

change in miles per hour while driving in the

city. Explain what the slope represents.

PHYSICAL SCIENCE The table below shows

the relationship between the number of seconds

y it takes to hear the thunder after a lightning

strike and the distance x you are from the

lightning.

WATER Graph the data. Then find the slope of

the line. Explain what the rate of change

represents.

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SNACKS The table below shows the number of

small packs of fruit snacks y per box x. Find the

rate of change. Explain what the slope

represents.

Find the rate of change for each table. Explain

what the slope represents.

The number of minutes included in different cell

phone plans and the costs are shown in the table.

What is the approximate rate of change in cost

per minute?

Find the rate of change for each graph. Explain

what the slope represents.

Find the rate of change for each graph. Explain

what it represents.

CYCLING The table shows the distance y

Cheryl traveled in x minutes while competing in

the cycling portion of a triathlon. Find the rate of

change. Explain what the slope represents.

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Make a Table and Find the Slope

1. Juan is on page 350 of his non-fiction book. He reads 12 pages a night.

a) Make a table showing what page Juan would be on after the 5th night.

b) Find the slope between the 2nd and 3rd night

c) What does the slope represent (in words)

d) Is the function linear? Explain why or why not.

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2. Cameron earns $100 every two weeks mowing lawns.

a) Make a table showing how much money he earns after 8 weeks.

b) Find the slope between the 4th and 8th week.



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3. Joe weighs 250 pounds. He is losing 8 pounds a week.

a) Make a table showing how much he weighs after 6 weeks.

b) Find the slope between the 3th and 4th week.



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SLOPE Check for Understanding

1. Juan is burning 27 calories for every 3 minutes that he runs on the treadmill. Create a

table that represents how many calories he burns over 21 minutes.

2. Is the function represented in your table linear? Justify your answer.

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Slope Real World Word Problem

Cell Phone Scenario

A certain cell phone package charges $39 even if 0 minutes are used during the month. Each

additional minute of talk time adds $.07 per minute.

Create an x-y chart to represent this function:

x

(minutes)

y

(dollars)

1. Where would the y-intercept be on a graph to represent this function? Explain your

reasoning.

2. Is this a linear function? How do you know?

3. Is there a constant rate of change? If so, what is it?

4. Would there be a point at the origin (0, 0)? Explain your reasoning.

5. Is the function continuous or discrete?

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SLOPE CONCEPT TASK

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Slope Formula – Performance Task

1. Reynaldo is planning to drive from San Ysidro to San Francisco in his car. Reynaldo started to fill out the

table below showing how far in miles he can travel for each gallon of gas he uses.

Gallons 2 4 6 10 12

Miles 30 90 120

Use the information in Reynaldo’s Table to ensure the questions below.

a. Find the rate of change to find how many miles per gallons Reynaldo’s car gets? State in words what the rate of change means in the context of the problem.

b. Complete the table for Reynaldo. Do it for the table above!

c. When Reynaldo’s tank is full, it holds 20 gallons. How far can Reynaldo drive on a full tank of gas?

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d. Graph the information from table above and use the graph to prove your findings from parts a and c.

1. Did you label all your axes?

2. Did you identify your findings from:

o Part a o Part c

Explain in words if your findings from parts a, b, and c remained the same or if they changed.

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Converting equations to slope-intercept form NOTES

Standard Form:

623 yx , an equation where both x

and y are on the ________side, and the

_____________ is on the right.

Slope-intercept bmxy

Rate of Change (m) The coefficient of x, this will tell us the

____________ over the _____________.

y-intercept (b)

The number part in the equation, it will tell us

where a line intersects (crosses) the _______-

axis.

What is the rate of change? _______

What is the y-intercept? _____


What is the y-intercept? _______

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Graphing equations in slope-intercept form NOTES

Slope-Intercept Formula

Rate of Change

y-intercept

x y

x y

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You Try:

You Try:

x y

You Try:

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x y

x y

You Try: You Try:

What is the equation of the graph below?

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Point-Slope, Slope-Intercept, Standard Form NOTES

Point-Slope Form

Slope-Intercept Form

Standard Form

Example:

Slope is 3

The point given is (1, 1)

Write an Equation in Point slope

formula

Make a graph

Example:

Slope is -1/2

The point given is (3, -2)

Write an Equation in Point slope

formula

Make a graph

Example:

Write and equation in Point Slope Form

m = 5/2

Point (-3, 0)

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You Try:


m = -7

Point (4, 2)

Example:


m = 2

Point (1/2, 1)

You Try:


m = -4

Point (-1, -2)

Write an equation in point slope form

given the two points below

(4. -7) and (0, 5)

Put your equation from above in slope

intercept form

Put your equation from above in

standard form



(1, -2) and (3, 10)


intercept form


standard form

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(6, 3) and (0, -1)


intercept form


standard form

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Writing Equations from graphs NOTES

Rate of Change

y-intercept

Example 1: Write the equation of the line.

What is the rate of change (m)?

What is the y-intercept (b)?

Write the equation of the line in Slope-Intercept and point

slope form.





slope form.


What is the slope (m)?



slope form.

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You Try: Write the equation of the line.




slope form.





slope form.





slope form.





slope form.





slope form.

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1. 2. 3.

Example 6 Rosa and Janet went kayaking. The cost to rent a kayak requires a $12 deposit and a rental fee of $3 per hour.

Identify the Rate of Change: What does it represent in the context of the situation? Identify the y-intercept: What does it represent in the context of the situation? Write an equation that represents the cost as a function of the number of hours. .

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YOU TRY: Margot want to have a birthday party at Chuck E Cheese. The cost for the package is $140 plus $15 per pizza.

Identify the slope: What does it represent in the context of the situation? Identify the y-intercept: What does it represent in the context of the situation? Write an equation that represents the cost as a function of the number of pizzas.

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Graphing Equations Check for Understanding The table shows the relationship between some Fahrenheit temperatures and their Celsius equivalents

Fahrenheit Celsius

-13 -25

-4 -20

5 -15

23 -5

32 0

50 10

68 20

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Algebra Support

Topic: Forms of equations of lines

Directions: Solve for y, you need to distribute and then solve the multi-step equation.

1. y – 8 = –2(x – 3) 2. y + 4 = 7(x – 8)

3. y + 10 = –(x – 3) 4. y + 9 = –4(x + 12)

5. y + 2 = 1

2(x + 4) 6. y – 3 =

1

4 (x + 8)

7. y – 18 = –6(x – 2) 8. y + 5 = 7(x – 1)

9. y – 14 = 3(x + 0) 10. y – 6 = 1

2 (x + 6)

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11. y + 1 = –8(x + 9) 12. y + 10 = –6(x + 1)

13. y – 2 = 1

4(x – 12) 14. y + 2 = –(x + 3)

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Writing Equations of a line NOTES

Coordinates

Slope Formula

Point-Slope Form

Slope-Intercept

Form

Example 1: Write the equation that has a

slope of 2 and passes through

the point (3, 4)

Example 2: Write the equation that has a

rate of change of -3 and passes

through the point (3, -1)

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Example 4: Write the equation that

describes this line in slope-

intercept form.

Your Try!!!

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Your Try!!!

Example 5:

Write an equation that

passes thru (8, 4) and

(6, -2)

Example 6:

You went to the annual

county fair this weekend.

Below is a table that shows

how much money you

spent.

a. Write a linear equation in which y represents the total

cost and x represents the number of rides selected.

b. What does the rate of change represent in the context of

the problem?

c. What could the y-intercept represent in the context of the

problem?

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You Try:

While your family is

visiting Lake Morena, you

and your brother decide to

go boating. The table

below shows the cost for

renting a boat.

a. Write a linear equation in which x represents the hours

for renting the canoe, and y represents is the total money

paid to rent the canoe.

b. What does the slope represent in the context of the

problem?

c. What could the y-intercept represent in the context of the

problem?

Example 7:

A caterer charges a $200

fee plus $20 per person

served.

a. Write an equation that represents the cost as a function of the

number of guests.

b. Create a graph to represent this relationship.

c. Identify the rate of change and y-intercept and describe their

meanings.

d. If 25 people are being invited and there is only $400 in the budget,

will they have enough money to pay for this many people?

e. How much would it cost for 8 people to be served by the caterer?

9 39

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You Try: The cost as a function

of the number of hours a closet

organizer worked is graphed

below.

a. Write an equation that represents the cost as a function of the

number of hours.

b. What does the slope represent in the context of the problem?

c. What could the y-intercept represent in the context of the problem?

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Writing Equations from a table Notes/Guided Practice

1. The data in the table shows the cost of renting a car by the day, including a deposit.

Renting a Car

Days (d) Cost in Dollars (c)

2 110

3 140

5 200

If days (d) were graphed on the horizontal axis and cost, c, were graphed on the vertical

axis, what would be the equation of a line that fits the data?

Slope = point – slope to slope intercept:

2. The data in the table shows the cost of renting a canoe by the hour, including a deposit.

Renting a Canoe

Hours (h) Cost in Dollars (c)

3 90

7 190

9 240

If hours h, were graphed on the horizontal axis and cost, c, were graphed on the vertical



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3. The data in the table shows the cost of renting roller skates by the hour, including a

deposit.

Renting roller skates

Hours (h) Cost in Dollars (c)

2 7

4 11

7 17

If hours h, were graphed on the horizontal axis and cost, c, were graphed on the vertical



4. The data in the table shows the cost of video games by the hour, including a deposit.

Renting a Video Game


2 25

3 35

4 45

If days (d) were graphed on the horizontal axis and cost, c, were graphed on the vertical


Slope = point – slope to slope-intercept:

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5. Which of the following equations is represented by the input/output box shown below?

x 0 1 2 3 4

y 4 1 -2 -5 -8

Slope: point – slope to slope-intercept:

A. xy 43

B. xy 43

C. xy 34

D. xy 34


x 0 1 2 3 4

y -3 -1 1 3 5

Slope: point – slope to slope-intercept:

A. 32 xy

B. 32 xy

C. 32 xy

D. 32 xy

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Writing Equations from a table with unit conversions NOTES

1. The data in the table shows the cost of

renting a car by the day, including a deposit.

Renting a Car

Days (d) Cost in

Dollars (c)

2 110

3 140

5 200

A. Write an equation in slope intercept form

where c represents the cost and d represents

the number of days:

B. Identify the slope and y-intercept and

explain what each means in the context of the

problem.

C. What would the cost of renting the car for

2 weeks?

2. The data in the table shows the cost of renting

a canoe by the hour, including a deposit.

Renting a Canoe

Hours (h) Cost in

Dollars (c)

3 90

7 190

9 240


where c represents the cost and h represents the

number of hours:

B. Identify the slope and y-intercept and explain

what each means in the context of the problem.

C. What would be the cost of renting the canoe

for 3 days?

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3.The data in the table shows the cost of

video games by the hour, including a deposit.

Renting a Video Game


2 25

3 35

4 45


where c represents the cost and d represents

the number of days:

B. Identify the slope and y-intercept and

explain what each means in the context of the

problem.

C. What would the cost of renting the video

for 1 week?

4. The data in the table shows the cost of renting

roller skates by the hour, including a deposit.

Renting roller skates

Hours (h) Cost in Dollars

(c)

2 7

4 11

7 17


where c represents the cost and h represents the

number of hours:

B. Identify the slope and y-intercept and explain

what each means in the context of the problem.

C. What would the cost of renting the roller

skates for 1 day?

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x 0 1 2 3 4

y 4 1 -2 -5 -8

E. xy 43

F. xy 43

G. xy 34

H. xy 34

6. A seed is planted 3 inches below the ground. It grows at a rate of 2 inches per week. Which equation

represents the situation?

E. 32 xy

F. 32 xy

G. 32 xy

H. 32 xy

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Writing Equations from a Table Classwork 1. The table below shows the cost (y) to play (x) games at the amusement park.

Number of Games, x 6 9 12 15

Cost in Dollars, y 4 5 6 7

a) What is the rate of change what does the rate of change mean in this context?

b) What is the y-intercept (the time when x = ___)? What does the y-intercept mean in this

context?

c) What is the equation of the line represented by this table? y = ____x + _______

2. The table to the right shows the amount of money Betty has in her bank account. Which

equation matches the table?

A. xxf 8)(

B. xxf8

1)(

C. 258)( xxf

D. 258

1)( xxf

In the problem above, what is the rate of change? What does the rate of change represent

in the context of this problem?

Months (x) 0 1 2 3 4

Money in Bank (y) 25 33 41 49 57

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3. The table below shows the amount of money Sam will earn (y) by shoveling (x) number of

driveways.

Number of Driveways (x) 0 1 2 3 4

Earnings in dollars (y) 10 13 16 19 22

a) What is the rate of change what does the rate of change mean in this context?

b) What is the y-intercept (the time when x = ___)? What does the y-intercept mean in this

context?

c) What is the equation of the line represented by this table? y = ____x + _______

4. The table to the right shows the number of pies Jimmy earns for selling pies. Which equation

matches the table?

A. xxf 5)(

B. xxf5

1)(

C. 511

1)( xxf

D. 115)( xxf

In the problem above, what is the rate of change? What does the rate of change represent

in the context of this problem?

Pies Sold (x) 0 1 2 3 4

Earnings in dollars (y) 11 16 21 26 31

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Writing Equations from a Story Classwork

1) Sam runs 5 miles before school every day to train for the big track meet. After school, he also runs at rate of

2 miles per hour. Which function below represents the total miles that Sam runs?

A. f(x) = 5x + 2

B. f(x) = 5x - 2

C. f(x) = 2x – 5

D. f(x) = 2x + 5

2) Tim earns $7 an hour working at McDonald’s. He also was given a signing bonus when he started of $25.

Which equation below represents Tim’s money?

A. f(x) = 25x – 7

B. f(x) = 25x + 7

C. f(x) = 7x + 25

D. f(x) = 7x – 25

3) Jane works as a waitress at the local Diner. Jane is paid a flat rate of $15 on the days she works. In addition

to her flat rate, she also earns $4 per hour in tips. Write an equation that represents the amount of money (y) that

Jane makes, for working x hours.

4) Joey goes to the amusement to ride as many rides as he can. Each ride costs $2. In addition to paying for each

ride, Joey must also pay admission into the park, which costs $8. Which equation below represents the amount

of money Joey will spend to ride x rides?

A. f(x) = 2x – 8

B. f(x) = 2x + 8

C. f(x) = 8x - 2

D. f(x) = 8x + 2

5) Fun Times Music is offering a big promotional sale. The store is selling a grocery bag for $25 – but once you

have the bag, any CD that you put into the bag will only cost your $2 more. What a deal! Which equation below

represents the cost of buying x CD’s?

A. f(x) = 25x – 2

B. f(x) = 25x + 2

C. f(x) = 2x + 25

D. f(x) = 2x

*** Tips for Success ***

Circle and underline important words. Look for the slope

by looking for those important key words we have above.

WRITE DOWN the m & b!!

m = _______ b = _________

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Slope and y-intercept in the context of word problems Pratice Sheet

You have a job that pays by the hour. On Monday, you worked 7 hours and earned $42.

On Tuesday, you worked 6 hours and earned $36.

1) Let x represent the number of hours worked and let y represent the amount earned. Write two

ordered pairs that represent the situation above.

(Hours worked, amount earned): ( , ) and ( , )

2) Plot the two points given by the ordered pair and draw a line through the points. Make sure

you label your graph.

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3) Find the slope of the line. What does it represent in the context of this situation?

4) Find the y-intercept of the line. What does it represent in the context of the situation?

5) How much would you earn if you worked 10 hours? _____

20 hours?_____

100 hours?_______

Explain how you are determining your answers.

6) Find the equation of the line passing through the 2 points. Explain how the equation is

represented in the context of the situation.

7) How would the equation be different if you received a $35 bonus for starting the job?

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You are an Internet provider that charges $10 a month plus an hourly fee to use the

Internet. One month you paid a total monthly bill of $16 for 2 hours of Internet time.

Another month, you paid a total monthly bill of $22 for 4 hours of Internet time.

Let x represent the number of hours and let y represent the total monthly bill. Write two ordered

pairs that represent this situation.

(Hours, total monthly bill): ( , ) and ( , )

9) Plot the two points given by the ordered pair on your graph paper and draw a line through the

points. Make sure you label your graph.

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10) Find the slope of the line. What does it represent in the context of this situation?

11) Find the y-intercept of the line. What does it represent in the context of the situation?

12) How much would your total bill be if you used the Internet for 6 hours?_______

7 hours?_______

10 hours?_______

20 hours? _______

13) Write an equation to represent the situation.

14) How would the equation be different if the Internet provider charged $30 a month in

addition to the hourly fee?

15) Explain how to find the equation of a line given two points. Like the examples above, create

a situation, plot the points, graph the line, find the slope, find the y-intercept, and write the

equation. Explain all your work.

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Multiple Representations Concept Task

Translate…Identify…. Create a table and a graph

Direction:

Problem:

3)

Marie wants to figure out how much money to bring to see a movie. She knows tickets cost $8.00 while each

snack cost $2.50 How much money will she need if she wants 5 snack, 10 snacks, or 15 snacks?

Equation: _______________________________________________________________________________

In words explain what: x = _________________________________________________________________

y = _________________________________________________________________

m = _________________________________________________________________

b = _________________________________________________________________

Create a table and graph.

2004 EduStic – “Learning That Sticks!”

Translate the word problem into slope-intercept form. Be able to identify the different parts of the

slope-intercept form (y = m x + b)

X Y= (X,Y)

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Writing Equations Concept Task

A trainer for a professional football team keeps track of the amount of water players consume

througough practice. The trainer observes that the amount of water consumed is a linear

function of the temperature on a given day. The trainer finds when it is 90°F the players

consume 220 gallons of water, and when it is 76° the players consume 178 gallons of water.

PART A: Write a linear function to model the relationship between the gallons of water

consumed and the temperature.

PART B: identify and explain what the x and y intercept would represent in the context of this

problem.

PART C: Explain the meaning of the slope in the context of the problem.

PART D: Graph the linear function.

http://www.google.com/url?sa=i&rct=j&q=first+quadrant+graph&source=images&cd=&cad=rja&docid=Q6o-fYJJHSLjvM&tbnid=Ga3NlvkuP4ETlM:&ved=0CAUQjRw&url=http://www.jamesrahn.com/graph paper/graph_paper.htm&ei=jEE5Uf2TC6SuyQHFtoGwCw&bvm=bv.43287494,d.aWc&psig=AFQjCNEALu6WFpBHtGPLbHjbJVy5jBmkKQ&ust=1362793212359574

P a g e | 106

PART E: Identify the domain and range of the function

Characteristics of Functions Practice

1. A taxi company in Atlanta charges $2.75 per ride plus $1.50 for every mile driven. Write the equation for the

line, and determine the key features of this function.

Equation: ____________ Discrete or Continuous: __________

Domain: _____________ Range: _______________

Intercepts: ___________ Increasing or Decreasing: ________

Max or Min: __________

2. A rental store charges $25 to rent a steam cleaner and $7 for each additional hour. Write the equation for

the line, and determine the key features of this function.

Equation: ____________ Discrete or Continuous: ___________

Domain: _____________ Range: _______________


Max or Min: __________

3. The cost of an air conditioner is $110. The cost to run the air conditioner is $0.35 per minute. Write the

equation, and determine the key features of this function.


Domain: _____________ Range: _______________

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Intercepts: ___________ Increasing or Decreasing: ________Max or Min: _________

4. A gear on a machine turns at a rate of 3 revolutions per second. Write the equation, and determine the key

features of this function.


Domain: _____________ Range: _______________


Max or Min: __________

5. Fill in the information for each graph.

a) b) c)

Equation:_____________ Equation: _____________ Equation: ______________

Domain: _____________ Domain: _____________ Domain: _____________

Range: ______________ Range: ______________ Range: ______________

Intercepts: ___________ Intercepts: ___________ Intercepts: ___________

Increasing / Decreasing: ______ Increasing / Decreasing: ______ Increasing / Decreasing: ____

Max or Min: __________ Max or Min: __________ Max or Min: __________

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Linear Functions and Multiple Representations

Mike’s dad gave him $500 toward a car. Mike is saving $200 each month. a) Make a table b) Write an equation c) Make a graph for this situation.

Is this function discrete or continuous?

Domain:

Range:

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Brenda is giving her baby a bath. She is filling the bathtub with water. Every 3 minutes she measures the height

of the water in the tub. At 3 minutes there were 2 inches of water. At 6 minutes there were 4 inches of water. a) Make a table b) Write an equation c) Make a graph for this situation.

Is this function discrete or continuous?

Domain:

Range:

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Parallel & Perpendicular lines

Parallel Lines

You Try:

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You Try:

Example 4: Determine the slope of the line parallel to the equation

Write an equation that is parallel to the line

to the left.

Example 5: Determine the rate of change of the line parallel to the equation


to the left.

You Try: Determine the slope of the line parallel to the equation


to the left.

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You Try: Determine the rate of change of the line parallel to the equation


to the left.

Perpendicular Lines

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Example 8: Determine the rate of change of the line perpendicular to the equation

Write an equation that is perpendicular to the

line to the left.

Example 9: Determine the slope of the line perpendicular to the equation


line to the left.

You Try: Determine the rate of change of the line perpendicular to the equation


line to the left.

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Example Write an equation in slope-intecerpt form for the line that passes through (-3, -1) and is perpendicular to the line y = 2x – 5.

YOU TRY

Write an equation in slope-intercept form for the line that passes through (–5, 3) and is perpendicular to the line given by y = 5x.

Example

Write an equation in slope-intercept form

for the line that passes through (–5, 3) and is parallel to the line given by y = 5x.

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graphing lines and writing equations of...

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