Mick is trying to determine whether the following two line are parallel.

Question

y = 2/3 x + 7
y = 2/3 x - 2

Which statement correctly describes the approach Mick should take bases on the best reasoning?

Statement #1: Mick says he should verify that the lines have the same slope but different intercepts.
Statement #2: Mick says he should verify that the lines have the same y-intercepts but different slope

Statement # __ describes the approach Mick should take based on the best reasoning

Answer 1

Statement #1 describes the approach Mick should take based on the best reasoning.

To determine if two lines are parallel, one should check if they have the same slope. For two lines to be considered parallel, they must have the same slope but different y-intercepts.

In this case, both lines are expressed in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept. Here, both equations have the same slope of \( \frac{2}{3} \) but different y-intercepts (7 and -2), indicating that the lines are indeed parallel.

Thus, Mick should verify that the lines have the same slope but different intercepts, making Statement #1 the correct choice.