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

Question

y=23x+7
𝑦
=
2
3
𝑥
+
7

y=23x−2
𝑦
=
2
3
𝑥
−
2

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

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

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

Answer 1

To determine whether two lines are parallel, you need to check their slopes. Lines are considered parallel if they have the same slope and different y-intercepts.

Looking at the given equations:

1. First pair of lines:

   • \( y = \frac{2}{3}x + 7 \)
   • \( y = \frac{2}{3}x - 2 \)
   • Both lines have the same slope of \(\frac{2}{3}\) but different y-intercepts (7 and -2). Therefore, these lines are parallel.

2. Second pair of lines:

   • \( y = 23x + 7 \)
   • \( y = 23x - 2 \)
   • Both lines have the same slope of 23 but different y-intercepts (7 and -2). Therefore, these lines are also parallel.

Given these analyses, the correct approach for Mick should be:

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

This statement accurately describes the condition needed to determine that two lines are parallel. Thus, Statement #1 is the correct choice.