Question

Marco is trying to determine whether the following two lines are parallel.

y=23x+7
𝑦
=
2
3
𝑥
+
7

y=23x−5
𝑦
=
2
3
𝑥
−
5

Which statement correctly describes the approach Marco should take based on the best reasoning?

Statement #1: Marco says he should verify that the lines have the same slope but different y-intercepts.

Statement #2: Marco says he should verify that the lines have the same y-intercept but different slopes.

Answer 1

Statement #1 is correct.

Parallel lines have the same slope but different y‑intercepts. If two lines share a y‑intercept but have different slopes, they meet at that intercept and are not parallel. For example, y = (2/3)x + 7 and y = (2/3)x − 5 are parallel because both slopes are 2/3 but the intercepts differ.