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© 2012 Pearson Education, Inc.. All rights reserved.
Section 1.1Slopes and
Equations of Lines
How are linear relationships used to model and solve real
world problems?
1 - 2 © 2012 Pearson Education, Inc.. All rights reserved.
Match each term to a correct description.
Terms Descriptions1. point-slope form A. Where x- and y- axes cross.
2. Horizontal line B. Graph with No slope
3. Vertical line C. Slopes are the same
4. Perpendicular lines D. x-coordinate is negative and y-coordinate is negative
5. Parallel lines E.
6. 2nd Quadrant F. Has two axes and four quandrants
7. 3rd Quadrant G. Slopes are opposite reciprocals
8. Cartesian Coordinate Plane H. Graph has slope of zero
9. Origin I. x-coordinate is negative and y-coordinate is positive.
11 xxmyy
How are linear relationships used to model and solve real world problems?
1 - 3 © 2012 Pearson Education, Inc.. All rights reserved.
Quadrants
How are linear relationships used to model and solve real world problems?
1 - 4 © 2012 Pearson Education, Inc.. All rights reserved.
Intercepts & Slopes
How are linear relationships used to model and solve real world problems?
1 - 5 © 2012 Pearson Education, Inc.. All rights reserved.
How are linear relationships used to model and solve real world problems?
3,2 and 8,9given line theof slope theFind :Example
1 - 6 © 2012 Pearson Education, Inc.. All rights reserved.
Possible Slopes of lines
How are linear relationships used to model and solve real world problems?
1 - 7 © 2012 Pearson Education, Inc.. All rights reserved.
Your Turn 1 – Check for Understanding
Find the slope of the line through (1,5) and (4,6).
1 1 2 2 Let ( , ) (1,5) andSol ( ,ut )ion: (4,6). x y x y
Use the definition of the slope .ymx
6 54 1
13
How are linear relationships used to model and solve real world problems?
1 - 8 © 2012 Pearson Education, Inc.. All rights reserved.
Writing Equations
How are linear relationships used to model and solve real world problems?
1 - 9 © 2012 Pearson Education, Inc.. All rights reserved.
Examples: Find an equation of a line who passes through the points (8,9) and (-2,3)
How are linear relationships used to model and solve real world problems?
1 - 10 © 2012 Pearson Education, Inc.. All rights reserved.
Figure 5
How are linear relationships used to model and solve real world problems?
1 - 11 © 2012 Pearson Education, Inc.. All rights reserved.
Your Turn 2 – Check for Understanding
Find the equation of the line with x-intercept − 4 and y-intercept 6. Solution: Notice that b = 6. To find m, use the definition of the slope after writing the x-intercept as (− 4, 0) and y-intercept as (0,6).
Substituting these values into y = mx + b, we have
0 6 6 34 0 4 2
m
3 6.2
y x
How are linear relationships used to model and solve real world problems?
1 - 12 © 2012 Pearson Education, Inc.. All rights reserved.
Your Turn 3 – Check for Understanding
Find the slope of the line whose equation is 8 3 5.x y
To find the slope, solve the equatiSolution on f: or y.8 3 5x y
Subtract 8 from3 8 5 both sides. y x x
Divide both si8 5 3
des b 33
y . y x
The coefficient of is 8 / 3, which is the slope of the line. x
How are linear relationships used to model and solve real world problems?
1 - 13 © 2012 Pearson Education, Inc.. All rights reserved.
Your Turn 4 – Check for Understanding
Find the equation of the line through (2,9) and (5,3). Put your answer in slope-intercept form.
Begin by using the definition of slope of the line that passes through the giveSo
n lution
poi:
nts.3 9 6 25 2 3
m
Either (2,9) or (5,3) can be used in the point-slope form with 2.m
1 1
1 1
1 1
If ( , ) (2,9), then ( )
9 2( 2)
9, 2, 2 y x
x yy y m x x
y m x
9 2 4 Distributiv e Propertyy x
2 13 Add 9 b ot h sidesy x
How are linear relationships used to model and solve real world problems?
1 - 14 © 2012 Pearson Education, Inc.. All rights reserved.
Assessment Prompt
Ones do Page 13 #1,7,11,15,19 Twos do Page 13 #3,5,9,17,21
Check each other’s work….Be prepared to defend your answers.
How are linear relationships used to model and solve real world problems?
1 - 15 © 2012 Pearson Education, Inc.. All rights reserved.
A Quick Review
How are linear relationships used to model and solve real world problems?
1 - 16 © 2012 Pearson Education, Inc.. All rights reserved.
Homework
Page 13 #2-12 even & #16-24 even
How are linear relationships used to model and solve real world problems?
1 - 17 © 2012 Pearson Education, Inc.. All rights reserved.
Parallel & Perpendicular lines
How are linear relationships used to model and solve real world problems?
1 - 18 © 2012 Pearson Education, Inc.. All rights reserved.
Your Turn 5
Find the equation of the line that passes through the point (4,5) and is parallel to the line 3 6 7.x y
The slope of 3 6 7 can be found by writing the equation in slope-intSolutio
ercept form.n
: x y
subtract 3 from both sides a3 6 7
6 3 7 3 7
nd
and divid 6 6
e both sides by 6.
1 72 6
xx y
y x
y x
y x
The result shows that the slope is 1/ 2. Since the linesare parallel, 1/ 2 is also the slope of the line whose equationwe want. cont inued
How are linear relationships used to model and solve real world problems?
1 - 19 © 2012 Pearson Education, Inc.. All rights reserved.
Your Turn 5 continued
1 1
1 1
This line passes through (4,5). Substituting 1/ 2,4 and 5 into the point-slope form give
(s
)y
mx y
y m x x
1 1
1 1
This line passes through (4,5). Substituting 1/ 2,4 and 5 into the point-slope form giv s
( ).e
y xx
y
m
m xy
1 2 5 Add 5 to both sid e .2
sy x
1 3 2
y x
How are linear relationships used to model and solve real world problems?
1 - 20 © 2012 Pearson Education, Inc.. All rights reserved.
Your Turn 6
Find the equation of the line that passes through the point (3,2) and is perpendicular to the line 2 3 4.x y
To find the slope, write 2 3 4 in slope-intSolut
erceion
pt r:
m:
fox y
subtract 2 from both sides2 3 43 2 4
2 4 3 3
and
and divide both sides by 3.
x yy x
y
x
x
The slope is 2 / 3. Since the lines are perpendicular, if line 2has slope , then 1
33 / 2. continued
L
m m
m
How are linear relationships used to model and solve real world problems?
1 - 21 © 2012 Pearson Education, Inc.. All rights reserved.
Your Turn 6 continued
1 1
1 1
Now subtitute 3 / 2, 3 and 2 into the point-slope( )
form.y y m
m x yx x
32 ( 3)2
y x
3 92 Distri 2
butive propert2
yy x
Add 2 to both sides and ge3 9 +2 2 23 5
t a
common de 2 2
nominator.
y x
y x
How are linear relationships used to model and solve real world problems?
1 - 22 © 2012 Pearson Education, Inc.. All rights reserved.
Assessment Prompt
Think-Pair-Share Page 13 #13,14,29,31,33 Check each other’s work….Be prepared to defend your
answers.
How are linear relationships used to model and solve real world problems?
1 - 23 © 2012 Pearson Education, Inc.. All rights reserved.
Applications
The table on the left lists the average annual cost (in dollars) of tuition and fees at public four-year colleges for selected years.
a) Plot the cost of public colleges by letting t = 0 correspond to 2000. Are the data exactly linear?
b) Use the points (0,3508) and (9,7020) to determine an equation that models the data.
c) How accurate is this equation in representing the cost of public colleges? Explain in context.
How are linear relationships used to model and solve real world problems?
1 - 24 © 2012 Pearson Education, Inc.. All rights reserved.
Graph of Tuition and Fees
How are linear relationships used to model and solve real world problems?
1 - 25 © 2012 Pearson Education, Inc.. All rights reserved.
Assessment Prompt
Think-Pair-Share Page 16 #71 Check each other’s work….Be prepared to defend your
answers.
How are linear relationships used to model and solve real world problems?
1 - 26 © 2012 Pearson Education, Inc.. All rights reserved.
Lesson Assignment
News/Talk Radio Math Modeling
Find a linear equation to model the number of stations carrying News/Talk Radio
Explain, in words, your process of finding this linear equation.
Predict the number of stations carrying news/talk radio in 2008. Compare this number with the actual amount.
Predict the number of stations carrying news/talk radio in 2020. How confidant can you be about your prediction?
How are linear relationships used to model and solve real world problems?
1 - 27 © 2012 Pearson Education, Inc.. All rights reserved.
Homework Pages 13-16 #26-38even, and
#50,52,58,62,64,66,68
How are linear relationships used to model and solve real world problems?
Exit Ticket:Why is slope important?