1. Copyright 2013, 2009, 2005, 2002 Pearson, Education, Inc.

2. 3.4
The Slope of a Line

3. Slope
Slope of a Line
The slope m of the line containing the points (x1, y1) and (x2, y2) is given by

4. Example
Find the slope of the line through (0, 3 ) and (2, 5). Graph the line.
If we let (x1, y1) be (0, 3) and (x2, y2) be (2, 5), then
upward

5. Example
Find the slope of the line containing the points (4, –3 ) and (2, 2). Graph the line.
If we let (x1, y1) be (4, –3) and (x2, y2) be (2, 2), then
downward

6. Helpful Hint
When finding slope, it makes no difference which point is identified as (x1, y1) and which is identified as (x2, y2). Just remember that whatever y-value is first in the numerator, its corresponding x-value is first in the denominator.

7. Slope-Intercept Form
When a linear equation in two variables in written in slope-intercept form,
y = mx + b
then m is the slope of the line and (0, b) is the y-intercept of the line.
slope
y-intercept is (0, b)

8. Example Find the slope and the y-intercept of the line
Solve the equation for y.
The slope of the line is 3/2 and the y-intercept is (0, 11/2).

9. Example Find the slope of the line x = 6. Vertical line
Use two points (6, 0) and (6, 3).
The slope is undefined.

10. Example Find the slope of the line y = 3. Horizontal line
Use two points (0, 3) and (3, 3).
The slope is zero.

11. Slopes of Vertical and Horizontal Lines
The slope of any vertical line is undefined. The slope of any horizontal line is 0.

12. Appearance of Lines with Given Slopesx y
Positive Slope
Line goes up to the right
Lines with positive slopes go upward as x increases.
m > 0
Lines with negative slopes go downward as x increases.
Negative Slope
Line goes downward to the right x y
m < 0

13. Appearance of Lines with Given Slopesx y
Zero Slope
horizontal line x y
Undefined Slope
vertical line

14. Parallel Lines
Two nonvertical lines are parallel if they have the same slope and different y-intercepts. x y

15. Perpendicular Lines
Two nonvertical lines are perpendicular if the product of their slopes is –1. x y

16. Parallel and Perpendicular Lines
Example
Are the following lines parallel, perpendicular, or neither.
–5x + y = –6
x + 5y = 5
Find the slope of each line.
The first equation has a slope of 5 and the second equation has a slope of 1/5, so the lines are perpendicular.