SWBAT… Write lines in slope-intercept form Monday, 1/11/09

Agenda1. WU (5 min)2. 3 examples of slope as rate of change (10 min)3. Cornell notes on “slope-intercept form” (30

min)

Warm-Up1. Place “hw#1: Slope” in a pile on your desks2. Complete vocabulary note card – “Slope”3. Start problems on back of agenda

HW #2: Writing Equations in slope-intercept

WARM-UP – ON THE BACK OF AGENDA!!!Frank had 5 gallons of gasoline in his bike.  After driving 100 miles, he had 3 gallons left. 

a. Find the slope of the lineb. What does this slope tell us?

Slope as the rate of changeSlope as the rate of change

a. Find the slope of the line    Slope = rise/run = -2/100 = -1/50

   b.  What does this slope tell us?Since -1/50 = -0.02, we know that Frank’s bike is burning 0.02 gallons of gasoline for every mile that he travels.   (The negative value of the slope tells us that the amount of gasoline in the tank is decreasing.)

Four students are renting a car for a road trip. The cost of renting the car is given by the function C = 12.5 + 21d, where C is the total cost for renting the car for d days. What does the slope of the function represent?

1. 2. cost per day3. 4.

The cost of prints from an online photo processor is given by C(p) = 29.99 + 0.13p. $29.99 is the cost of membership, and p is the number of 4-inch by 6-inch prints. What does the slope represent?1. cost per print2. cost of the membership3. cost of the membership and 1 print4. number of prints

Non-Linear EquationsNon-Linear Equationshttp://en.wikipedia.org/wiki/File:Graph_of_sliding_derivative_line.gif

Monday, 1/4 Tuesday, 1/5 Wednesday, 1/6 Thursday, 1/7 Friday, 1/8

Get ready for Ch 4 Slope ½ Day: A Slope Slope

Monday, 1/11 Tuesday, 1/12 Wednesday, 1/13 Thursday, 1/14 Friday, 1/15

Writing equations oflines in slopeintercept form (y=mx+b)

Graphing linearfunctions usingy=mx+b

½ Day: B Graphing linearfunctions usingy=mx+b (cont’d)

Writing equationsof lines in slopeinterceptform

Monday, 1/18 Tuesday, 1/19 Wednesday, 1/20 Thursday, 1/21 Friday, 1/22

MLKNO CLASSES

Writing equationsof lines in slopeinterceptform (cont’d)

Writing equationsof lines in slopeinterceptform (cont’d)

Final studyguide review

Final study guide review

Monday, 1/25 Tuesday, 1/26 Wednesday, 1/27 Thursday, 1/28 Friday, 1/29

ALGEBRA FINAL

Point slope form &

Standard form

All 3 forms of lines1. Slope-intercept2. Point-slope 3. Standard

END OF Q2END OF

SEMESTER1NO CLASSES

When an equation is in slope-intercept When an equation is in slope-intercept form:form:

What is the slope? ____________

2 1y x Now look at the equation below……

What is the y-intercept? ____________

Given y = ½x + ¾, what is the slope and the y-intercept?

m = ½b = ¾

Given y = ½x – ¾, what is the slope and the y-intercept?

m = ½b = -¾

Given y = -½x – ¾, what is the slope and the y-intercept?

m = -½b = -¾

1.) What is the slope? .102.) What is the meaning of the slope?3.) What is the y-intercept. b = 5 4.) What is the meaning of the y-intercept?5.) Write the equation of the line. y = .10x + 5

Total Cost of Cellular Phone Service

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Minutes

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• y = mx+ b is an equation that defines a line

• A line has two characteristics– Points that fall on the line– Slope

1.) What is the slope? 2.) What is the meaning of the slope?3.) What is the y-intercept (write as an ordered pair) 4.) What is the meaning of the y-intercept?5.) Write the equation of the line (y = mx + b).

Total Cost of Cellular Phone Service

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Minutes

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lars

Converting linear Converting linear equations into Slope-equations into Slope-

Intercept FormIntercept Form

4 Examples4 Examples

Slope intercept form is:

y = mx + b

Our main goal is to get the y alone on one side of the equation

Example 1 - convert into Example 1 - convert into Slope-InterceptSlope-Intercept Form Form

2 4 2y x 2 2

2 4 2y x 2 2 2

(divide both sides by 2 to get y alone)2 4 2y x

(now simplify all fractions)2 1

2 1y x What is the slope? _____ What is the y-intercept? ______

*** Your turn – Example 2 – convert to Slope-Intercept Form ***

-3y = -9x – 12

Step 1: divide both sides by -3 to get y alone

Step 2: Simplify all fractions

Step 3: Write your equation in y = mx + bWhat is the slope? ____________

What is the y-intercept? ____________

*** Check Your Answer ***

-3y = -9x – 12 (divide both sides by -3 to get y alone)

(now simplify all fractions)

y = 3x + 4

-3 -3

-3y = -9x – 12-3 -3 -3

Slope = 3

Intercept = 4

Wow, you’re good at this!!

***Example 3*** Convert to Slope-Intercept Form

21x – 7y =14 (subtract both sides by 21x)

-7y = -21x + 14(now divide both sides by -7)

y = 3x – 2

(simplify all fractions)

21 -21xx

7 - 7 -7

What is the slope? _________

What is the y-intercept? ________

2y + 26 = -6x

Step 1: Subtract both sides by 26

Step 2: Divide both sides by 2 to get y by itself

Step 3: Simplify all fractions

EXIT SLIP Convert to Slope-Intercept Form

***

What is the slope? ____________

What is the y-intercept? ____________

2y + 26 = -6x (subtract both sides by 26)

2y = -6x – 26(now divide both sides by 2

y = -3x – 13

(simplify all fractions)

You are a math wizard!

*** Check Your Answer ***

26 -26

2 2 2

In the standard (x, y) coordinate plane, what is the slope of the line given by the equation 5x – 4y = 3?