Question

Using the Point-Slope Form of a Line
Which statements are correct steps in finding the linear equation of a line that passes through the points (−1, 7) and (2, 4) using the point-slope form method? Select all that apply.

y = x + 6
7 = –1(–1) + b
y – 4 = –1 (x – 2)
y – 7 = –1 (x – (–1))
y – 2 = x – 4
y = –x + 6

Answer 1

Correct choices: 2, 3, 4, 6.

Reasoning:
- Slope m = (4 − 7)/(2 − (−1)) = −3/3 = −1.
- 3) y − 4 = −1(x − 2) — point-slope using (2,4). Correct.
- 4) y − 7 = −1(x − (−1)) = −1(x + 1) — point-slope using (−1,7). Correct.
- 2) 7 = −1(−1) + b — plugging (−1,7) into y = mx + b to solve for b is a valid step (gives b = 6). Correct.
- 6) y = −x + 6 — the line simplified to slope-intercept form. Correct.

Incorrect:
- 1) y = x + 6 — wrong slope.
- 5) y − 2 = x − 4 — wrong slope and doesn't use the given points.