EXAMPLE 2 Write an equation given two points

Write an equation of the line that passes through (–2, 5) and (2, –1).

SOLUTION

Calculate the slope.

3m = y2 – y1x2 – x1

= –1 – 52 – (–2)

= –64

= – 2

Find the y-intercept. Use the slope and the point (–2, 5).

y = mx + b Write slope-intercept form.

STEP 1

STEP 2

EXAMPLE 2

5 = – 32

(–2) + b

2 = b Solve for b.

Write an equation of the line.

y = mx + b Write slope-intercept form.

Substitute – 32

for m and 2 for b.y = – 32 x + 2

STEP 3

Substitute – for m, –2 for x, and 5 for y.

32

Write an equation given two points

EXAMPLE 3

Which function has the values f(4) = 9 and f(–4) = –7?

C f (x) = 2x – 13

m =y2 – y1

x2 – x1= –7 – 9

–4 – 4 = –16–8 = 2

D f (x) = 2x – 14

B f (x) = 2x + 1

Find the y-intercept. Use the slope and the point (4, 9).y = mx + b Write slope-intercept form.

EXAMPLE 3 Standardized Test Practice

f (x) = 2x + 10A

STEP 1 Calculate the slope. Write f (4) = 9 as (4, 9) and f (–4) = –7 as (–4, –7).

STEP 2

Substitute 2 for m, 4 for x, and 9 for y.9 = 2(4) + b

1 = b Solve for b.

Write an equation for the function. Use function notation.

f (x) = 2x + 1 Substitute 2 for m and 1 for b.

ANSWER

The answer is B. A C DB

EXAMPLE 3 Standardized Test Practice

STEP 3

GUIDED PRACTICE for Examples 2 and 3

2. Write an equation of the line that passes through (1, –2) and (–5, 4).

y = –x – 1ANSWER

GUIDED PRACTICE for Examples 2 and 3

3. Write an equation for the linear function with values f(–2) = 10 and f(4) = –2?

y = –2x + 6ANSWER