example 2 write an equation given two points write an equation of the line that passes through...
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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