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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
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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?
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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.)
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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.
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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
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Non-Linear EquationsNon-Linear Equations
http://en.wikipedia.org/wiki/File:Graph_of_sliding_derivative_line.gif
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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
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When an equation is in slope-intercept When an equation is in slope-intercept form:form:
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? ____________
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Given y = ½x + ¾, what is the slope and the y-intercept?
m = ½b = ¾
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Given y = ½x – ¾, what is the slope and the y-intercept?
m = ½b = -¾
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Given y = -½x – ¾, what is the slope and the y-intercept?
m = -½b = -¾
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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
4.905.005.105.205.305.405.505.605.705.80
0 1 2 3 4 5 6 7
Minutes
Do
llars
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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
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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
4.905.005.105.205.305.405.505.605.705.80
0 1 2 3 4 5 6 7
Minutes
Do
llars
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Converting linear Converting linear equations into Slope-equations into Slope-
Intercept FormIntercept Form
Converting linear Converting linear equations into Slope-equations into Slope-
Intercept FormIntercept Form
4 Examples4 Examples4 Examples4 Examples
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Slope intercept form is:
y = mx + b
Our main goal is to get the y alone on one side of the equation
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Example 1 - convert into Example 1 - convert into Slope-InterceptSlope-Intercept Form FormExample 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? ______
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*** 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 + b
What is the slope? ____________
What is the y-intercept? ____________
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*** 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!!
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***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? ________
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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? ____________
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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
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In the standard (x, y) coordinate plane, what is the slope of the line given by the equation 5x – 4y = 3?