P a g e | 1
Graphing Lines and
Writing Equations of
Lines
Name_____________________________
Math Teacher______________________________
P a g e | 2
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:
P a g e | 3
Date:
List the domain and range
Date: List all intervals where the graphs are increasing and decreasing.
a. b. c.
P a g e | 4
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?
P a g e | 5
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.
P a g e | 6
Linear Function: The Line
Formulas Slope: Slope-Intercept Form: Standard Form: Point-Slope Form:
P a g e | 7
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?
P a g e | 8
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.
P a g e | 9
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)
P a g e | 10
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.
P a g e | 11
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
P a g e | 12
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)}
P a g e | 13
Example 3
State the domain and range
Is the relation a function?
You Try
State the domain and range.
Is the relation a function?
{(8, 2), (–4, 1), (–6, 2),(1, 9)}
You Try
State the domain and range.
Is the relation a function?
Vertical Line Test
EXAMPLE
State the domain and range.
Is the relation a function?
P a g e | 14
You Try
State the domain and range.
Is the relation a function?
You Try
State the domain and range.
Is the relation a function?
You Try
State the domain and range.
Is the relation a function?
You Try
State the domain and range.
Is the relation a function?
You Try
State the domain and range.
Is the relation a function?
P a g e | 15
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) }
P a g e | 16
P a g e | 17
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?
P a g e | 18
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
P a g e | 19
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.
Is the data discrete or continuous? Explain.
You Try:
Is the data discrete or continuous? Explain.
You Try:
Is the data discrete or continuous? Explain.
P a g e | 20
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.
P a g e | 21
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?
4) Domain 5) Domain 6) Domain
Range Range Range
Function? Function? Function?
7) Domain 8) Domain 9) Domain
Range Range Range
Function? Function? Function?
P a g e | 22
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:
P a g e | 23
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
P a g e | 24
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.
P a g e | 25
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 ( , )
The x-intercept of the graph is ( , )
The y-intercept of the graph is ( , )
P a g e | 26
The x-intercept of the graph is ( , )
The y-intercept of the graph is ( , )
You Try! Find the x- and y-intercepts.
The x-intercept of the graph is ( , )
The y-intercept of the graph is ( , )
You Try!
The x-intercept of the graph is ( , )
The y-intercept of the graph is ( , )
The x-intercept of the graph is ( , )
The y-intercept of the graph is ( , )
P a g e | 27
Step 1 Find the intercepts.
The x-intercept of the graph is ( , )
The y-intercept of the graph is ( , ) Step 2: Graph the intercepts:
Step 1 Find the intercepts.
The x-intercept of the graph is ( , )
The y-intercept of the graph is ( , ) Step 2: Graph the intercepts:
P a g e | 28
P a g e | 29
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?
P a g e | 30
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.
P a g e | 31
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.
P a g e | 32
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?
P a g e | 33
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?
P a g e | 34
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?
P a g e | 35
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?
P a g e | 36
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
P a g e | 37
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.
P a g e | 38
P a g e | 39
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.
Matching Graph ______
3. The car’s speed increases sharply.
Matching Graph ______
4. The car’s speed decreases gradually.
Matching Graph ______
5. The car’s speed decreases suddenly.
Matching Graph ______
6. Describe what it means for the graph of the car’s speed to be a horizontal line?
P a g e | 40
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:
P a g e | 41
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
P a g e | 42
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)?
P a g e | 43
Summary:
P a g e | 44
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.
.
P a g e | 45
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 meaning of the slope?
What is the y intercept?
What does the y intercept represent?
What is the slope?
What is the meaning of the slope?
What is the y intercept?
What does the y intercept represent?
P a g e | 46
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
P a g e | 47
Look at the Card Set Graphs and the Interpretations. Place the letter of the appropriate Graph
and Interpretation in the organizer.
P a g e | 48
P a g e | 49
P a g e | 50
Relating Graphs to Stories-Interpreting Distance Time Graph Story Table
P a g e | 51
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).
P a g e | 52
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
Find the rate of change of
the line. What does it
represent in the context of
this situation?
You try 4
Find the rate of change of
the line. What does it
represent in the context of
this situation?
P a g e | 53
P a g e | 54
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.
P a g e | 55
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.
P a g e | 56
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.
P a g e | 57
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.
c) What does the slope represent (in words)
d) Is the function linear? Explain why or why not.
P a g e | 58
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.
c) What does the slope represent (in words)
d) Is the function linear? Explain why or why not.
P a g e | 59
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.
P a g e | 60
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?
P a g e | 61
SLOPE CONCEPT TASK
P a g e | 62
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?
P a g e | 63
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.
P a g e | 64
P a g e | 65
P a g e | 66
P a g e | 67
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 rate of change? _______
What is the y-intercept? _______
P a g e | 68
What is the rate of change? _______
What is the y-intercept? _______
What is the rate of change? _______
What is the y-intercept? _______
What is the rate of change? _______
What is the y-intercept? _______
What is the rate of change? _______
What is the y-intercept? _______
P a g e | 69
P a g e | 70
Graphing equations in slope-intercept form NOTES
Slope-Intercept Formula
Rate of Change
y-intercept
x y
x y
P a g e | 71
You Try:
You Try:
x y
You Try:
P a g e | 72
x y
x y
You Try: You Try:
What is the equation of the graph below?
P a g e | 73
P a g e | 74
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)
P a g e | 75
You Try:
Write and equation in Point Slope Form
m = -7
Point (4, 2)
Example:
Write and equation in Point Slope Form
m = 2
Point (1/2, 1)
You Try:
Write and equation in Point Slope Form
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
Write an equation in point slope form
given the two points below
(1, -2) and (3, 10)
Put your equation from above in slope
intercept form
Put your equation from above in
standard form
P a g e | 76
Write an equation in point slope form
given the two points below
(6, 3) and (0, -1)
Put your equation from above in slope
intercept form
Put your equation from above in
standard form
P a g e | 77
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.
Example 2: 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.
Example 3: Write the equation of the line.
What is the slope (m)?
What is the y-intercept (b)?
Write the equation of the line in Slope-Intercept and point
slope form.
P a g e | 78
You Try: Write the equation of the line.
What is the slope (m)?
What is the y-intercept (b)?
Write the equation of the line in Slope-Intercept and point
slope form.
You Try: 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.
Example 4: Write the equation of the line.
What is the slope (m)?
What is the y-intercept (b)?
Write the equation of the line in Slope-Intercept and point
slope form.
Example 5: 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.
You Try: 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.
P a g e | 79
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. .
P a g e | 80
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.
P a g e | 81
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
P a g e | 82
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)
P a g e | 83
11. y + 1 = –8(x + 9) 12. y + 10 = –6(x + 1)
13. y – 2 = 1
4(x – 12) 14. y + 2 = –(x + 3)
P a g e | 84
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)
P a g e | 85
Example 4: Write the equation that
describes this line in slope-
intercept form.
Your Try!!!
P a g e | 86
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?
P a g e | 87
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
P a g e | 88
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?
P a g e | 89
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
axis, what would be the equation of a line that fits the data?
Slope = point – slope to slope intercept:
P a g e | 90
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
axis, what would be the equation of a line that fits the data?
Slope = point – slope to slope intercept:
4. The data in the table shows the cost of video games by the hour, including a deposit.
Renting a Video Game
Days (d) Cost in Dollars (c)
2 25
3 35
4 45
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:
P a g e | 91
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
6. Which of the following equations is represented by the input/output box shown below?
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
P a g e | 92
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
A. Write an equation in slope intercept form
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?
P a g e | 93
3.The data in the table shows the cost of
video games by the hour, including a deposit.
Renting a Video Game
Days (d) Cost in Dollars (c)
2 25
3 35
4 45
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 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
A. Write an equation in slope intercept form
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?
P a g e | 94
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
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
P a g e | 95
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
P a g e | 96
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
P a g e | 97
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 = _________
P a g e | 98
P a g e | 99
P a g e | 100
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.
P a g e | 101
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?
P a g e | 102
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.
P a g e | 103
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.
P a g e | 104
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)
P a g e | 105
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.
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: _______________
Intercepts: ___________ Increasing or Decreasing: ________
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.
Equation: ____________ Discrete or Continuous: ___________
Domain: _____________ Range: _______________
P a g e | 107
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.
Equation: ____________ Discrete or Continuous: ___________
Domain: _____________ Range: _______________
Intercepts: ___________ Increasing or Decreasing: ________
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: __________
P a g e | 108
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:
P a g e | 109
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:
P a g e | 110
Parallel & Perpendicular lines
Parallel Lines
You Try:
P a g e | 111
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
Write an equation that is parallel to the line
to the left.
You Try: Determine the slope of the line parallel to the equation
Write an equation that is parallel to the line
to the left.
P a g e | 112
You Try: Determine the rate of change of the line parallel to the equation
Write an equation that is parallel to the line
to the left.
Perpendicular Lines
P a g e | 113
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
Write an equation that is perpendicular to the
line to the left.
You Try: Determine the rate of change of the line perpendicular to the equation
Write an equation that is perpendicular to the
line to the left.
P a g e | 114
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.
P a g e | 115