Question

A geometry class is asked to find the equation of a line that is parallel to y – 3 = −(x + 1) and passes through (4, 2). Trish states that the parallel line is y – 2 = –1(x – 4). Demetri states that the parallel line is y = –x + 6.

Are the students correct? Explain.

Trish is the only student who is correct; the slope should be –1, and the line passes through (4, 2).
Demetri is the only student who is correct; the slope should be –1, and the y-intercept is 6.
Both students are correct; the slope should be –1, passing through (4, 2) with a y-intercept of 6.
Neither student is correct; the slope of the parallel line should be 1.

Answer 1

Both students are correct.

Start with the given line: y − 3 = −(x + 1) → y − 3 = −x − 1 → y = −x + 2, so the slope is −1. A line parallel to this through (4,2) has slope −1, so in point–slope form:
y − 2 = −1(x − 4) — Trish's equation.

Rearrange Trish's form: y − 2 = −x + 4 → y = −x + 6, which is Demetri's equation. They are the same line (slope −1, y‑intercept 6), so the correct choice is: "Both students are correct; the slope should be −1, passing through (4, 2) with a y-intercept of 6."