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

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

Answer 1

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

Let's analyze the lines given:

1. \( y = \frac{23}{1}x + 7 \) (slope = \( \frac{23}{1} \))
2. \( y = \frac{2}{3}x + 7 \) (slope = \( \frac{2}{3} \))

And:

1. \( y = \frac{23}{1}x - 2 \) (slope = \( \frac{23}{1} \))
2. \( y = \frac{2}{3}x - 2 \) (slope = \( \frac{2}{3} \))

In both cases, the slopes (\(\frac{23}{1}\) and \(\frac{2}{3}\)) are different, thus the lines cannot be parallel.

Therefore, the correct statement is:

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

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