CHAPTER 3 Graphs of Liner Equations Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc....
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Transcript of CHAPTER 3 Graphs of Liner Equations Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc....
CHAPTER
3Graphs of Liner Equations
Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
3.1 Graphs and Applications of Linear Equations
3.2 More with Graphing and Intercepts
3.3 Slope and Applications
3.4 Equations of Lines
3.5 Graphing Using the Slope and the y-Intercept
3.6 Parallel and Perpendicular Lines
3.7 Graphing Inequalities in Two Variables
OBJECTIVES
3.3 Slope and Applications
Slide 3Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
a Given the coordinates of two points on a line, find the slope of the line, if it exists.
b Find the slope of a line from an equation.c Find the slope, or rate of change, in an applied
problem involving slope.
We have looked at two forms of a linear equation, Ax + By = C and y = mx + b
We know that the y-intercept of a line is (0, b).
y = mx + b
? The y-intercept is (0, b).
What about the constant m? Does it give certain information about the line?
3.3 Slope and Applications
a Given the coordinates of two points on a line, find the slope of the line, if it exists.
Slide 4Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
Look at the following graphs and see if you can make any connections between the constant m and the “slant” of the line.
y
x
21
3y x
y
x10
13
y x
y
x2
13
y x
y
x
31
10y x
3.3 Slope and Applications
a Given the coordinates of two points on a line, find the slope of the line, if it exists.
Slide 5Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
The slope of the line containing points (x1, y1) and (x2, y2) is given by
2 1
2 1
rise change in .
run change in
y yym
x x x
3.3 Slope and Applications
Slope
Slide 6Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLE
Solution rise change in Slope = =
run change in
y
x
1 5
4 4 =
( )
6
= 8
3or
4
2 1
2 1
y y
x x
3.3 Slope and Applications
a Given the coordinates of two points on a line, find the slope of the line, if it exists.
A Graph the line containing the points (4, 5) and (4, 1) and find the slope.
(continued)
Slide 7Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLE
Solution
rise
run
3.3 Slope and Applications
a Given the coordinates of two points on a line, find the slope of the line, if it exists.
A Graph the line containing the points (4, 5) and (4, 1) and find the slope.
Slide 8Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
The slope of a line tells how it slants.A line with a positive slope slants up from left to right. The larger the slope, the steeper the slant.
A line with a negative slope slants downward from left to right.
3.3 Slope and Applications
a Given the coordinates of two points on a line, find the slope of the line, if it exists.
Slide 9Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
The slope of the line y = mx + b is m. To find the slope of a nonvertical line, solve the linear equation in x and y for y and get the resulting equation in the form y = mx + b.
The coefficient of the x-term, m is the slope of the line.
It is possible to find the slope of a line from its equation.
3.3 Slope and Applications
Determining Slope from the Equation y = mx + b
Slide 10Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLE
m = 1 = Slope
a. b.
c. y = x + 8 d.
24
3y x
2
3y x
0.25 6.8y x
m = 4 = Slopem = = Slope
m = 0.25 = Slope
2
3
3.3 Slope and Applications
b Find the slope of a line from an equation.
B Find the slope of the line.
Slide 11Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLEWe solve for y to get the equation in the form y = mx + b.
3x + 5y = 15 5y = –3x + 15
3 15
5
xy
3
53y x
The slope is3
.5
3.3 Slope and Applications
b Find the slope of a line from an equation.
C Find the slope of the line 3x + 5y = 15.
Slide 12Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
5
15
5
3
xy
EXAMPLESolutionConsider the points (3, 3) and (2, 3), which are on the line.
A horizontal line has slope 0.
2 (
3
)
3
3m
0
5 0
(3, 3) (2, 3)
3.3 Slope and Applications
b Find the slope of a line from an equation.
D Find the slope of the line y = 3.
Slide 13Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLESolutionConsider the points (2, 4) and (2, 2), which are on the line.
The slope of a vertical line is undefined.
2 2
4 ( 2)m
6
undefined0
(2, 4)
(2, 2)
3.3 Slope and Applications
b Find the slope of a line from an equation.
E Find the slope of the line x = 2.
Slide 14Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
The slope of a horizontal line is 0.
The slope of a vertical line is not defined.
3.3 Slope and Applications
Slope 0; Slope Not Defined
Slide 15Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
Applications of Slope
Some applications use slope to measure the steepness. For examples, numbers like 2%, 3%, and 6% are often used to represent the grade of a road, a measure of a road’s steepness. That is, a 3% grade means that for every horizontal distance of 100 ft, the road rises or drops 3 ft.
3.3 Slope and Applications
c Find the slope, or rate of change, in an applied problem involving slope.
Slide 16Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLE
0.42 ft5.5 ft
0.4
.5
2
5m
420
5500
427.6%
550
The grade of the treadmill is 7.6%.** Reminder: Grade is slope expressed as a percent.
Solution
3.3 Slope and Applications
c Find the slope, or rate of change, in an applied problem involving slope.
F Find the slope (or grade) of the treadmill.
Slide 17Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
