Beginning Algebra, 11th Edition

We can summarize this discussion as follows.

Slope is a single number that allows us to determine the direction in which

a line is slanting from left to right, as well as how much slant there is to

the line.

200 CHAPTER 3 Linear Equations and Inequalities in Two Variables; Functions

Finding the Slope of a Line

Find the slope of the line in FIGURE 19.

We use the two points shown on the line. The

vertical change is the difference in the y-values, or

, and the horizontal change is the

difference in the x-values, or. Thus, the

line has

Counting grid squares, we begin at point Pand count

down4 grid squares. Then we count to the right

4 grid squares to reach point Q. Because we counted

down, we write the vertical change as a negative

number, - 4 here. The slope is - 44 ,or - 1. NOW TRY

slope=

change in y (rise)

change in x (run)

=

- 4

4

, or - 1.

6 - 2 = 4

- 1 - 3 =- 4

NOW TRY EXAMPLE 1

EXERCISE 1
Find the slope of the line.

(^06) Q (6, –1)
x
y
–1 4
2
4
–2
P (2, 3)
rise = –4
run = 4
2
FIGURE 19
x
y
(–2, –2)^0
(–1, 1)

NOTE The slope of a line is the same for any two points on the line.To see this,

refer to FIGURE 19. Find the points and on the line. If we start at

and count down2 units and then to the right2 units, we arrive at The slope is

or - 1 , the same slope we found in Example 1.

2

2 ,

1 5, 0 2.

1 3, 2 2 1 5, 0 2 1 3, 2 2

The idea of slope is used in many everyday situations. See FIGURE 20. A highway

with a 10%, or grade (or slope) rises 1 m for every 10 m horizontally. Architects

specify the pitch of a roof by using slope. A roof means that the roof rises 5 ft for

every 12 ft that it runs horizontally. The slope of a stairwell indicates the ratio of the

vertical rise to the horizontal run. The slope of the stairwell is 128 , or^23.

5 12

1

10 ,

12 ft

roof pitch

5 ft