Question

Which ordered pairs could be points on a line parallel to the line that contains (3, 4) and (–2, 2)? Check all that apply.

(–2, –5) and (–7, –3)
(–1, 1) and (–6, –1)
(0, 0) and (2, 5)
(1, 0) and (6, 2)
(3, 0) and (8, 2)

Answer 1

Slope of the line through (3, 4) and (–2, 2) is (4–2)/(3–(–2)) = 2/5. A parallel line must have slope 2/5.

Compute slopes:
- (–2, –5) and (–7, –3): (–3 – (–5))/(–7 – (–2)) = 2/–5 = –2/5 → no
- (–1, 1) and (–6, –1): (–1 – 1)/(–6 – (–1)) = –2/–5 = 2/5 → yes
- (0, 0) and (2, 5): (5–0)/(2–0) = 5/2 → no
- (1, 0) and (6, 2): (2–0)/(6–1) = 2/5 → yes
- (3, 0) and (8, 2): (2–0)/(8–3) = 2/5 → yes

Answer: (–1, 1) and (–6, –1); (1, 0) and (6, 2); (3, 0) and (8, 2).