Easy Algebra Step-by-Step

The Cartesian Coordinate Plane 179

Problem Find the slope of the line through the points shown.

10

y

x

9 8 7 6 5 4 3 2 1

–10–9–8–7–6–5–4–3–2–1 1 2 3 4 5 6 7 8

(7, 5)

(–4, –6)

–1^910

–2

–3

–4

–5

–6

–7

–8

–9

–10

0

Solution

Step 1. Specify (x 1 , y 1 ) and (x 2 , y 2 ) and identify values for x 1 , y 1 , x 2 , and y 2.

Let (x 1 , y 1 ) = (7, 5) and (x 2 , y 2 ) = (−4, −6). Then x 1 = 7, y 1 = 5,

x 2 = −4, and y 2 = −6.

Step 2. Evaluate the formula for the values from step 1.

m =

yy

xx

y 1

21 x

=

()−

()−

)− 5

)− 7

=

−

−

65 −

47 −

=

−

−

11

11

= 1

Step 3. State the slope.

The slope of the line that passes through the points (7, 5) and

(− 4 , − 6) i s 1. Note: The line slants upward from left to right—so the

slope should be positive.

Problem Find the slope of the line through the two points.

a. (−1, 4) and (5, −3)

b. (−6, 7) and (5, 7)

c. (5, 8) and (5, −3)