Write an equation given two points

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Writing Linear Equations Using Slope Intercept Form

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Write an equation given two points EXAMPLE 2 Write an equation given two points Write an equation of the line that passes through (–2, 5) and (2, –1). SOLUTION STEP 1 Calculate the slope. 3 m = y2 – y1 x2 – x1 = –1 – 5 2 – (–2) –6 4 – 2 STEP 2 Find the y-intercept. Use the slope and the point (–2, 5). y = mx + b Write slope-intercept form.

Write an equation given two points EXAMPLE 2 Write an equation given two points 5 = – 3 2 (–2) + b Substitute – for m, –2 for x, and 5 for y. 3 2 2 = b Solve for b. STEP 3 Write an equation of the line. y = mx + b Write slope-intercept form. y = – 3 2 x + 2 Substitute – 3 2 for m and 2 for b.

Standardized Test Practice EXAMPLE 3 EXAMPLE 3 Standardized Test Practice Which function has the values f(4) = 9 and f(–4) = –7? f (x) = 2x + 10 A B f (x) = 2x + 1 C f (x) = 2x – 13 D f (x) = 2x – 14 STEP 1 Calculate the slope. Write f (4) = 9 as (4, 9) and f (–4) = –7 as (–4, –7). m = y2 – y1 x2 – x1 = –7 – 9 –4 – 4 –16 –8 2 STEP 2 Find the y-intercept. Use the slope and the point (4, 9). y = mx + b Write slope-intercept form.

Standardized Test Practice EXAMPLE 3 Standardized Test Practice 9 = 2(4) + b Substitute 2 for m, 4 for x, and 9 for y. 1 = b Solve for b. STEP 3 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 D B

GUIDED PRACTICE for Examples 2 and 3 2. Write an equation of the line that passes through (1, –2) and (–5, 4). y = –x – 1 ANSWER

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 + 6 ANSWER