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

Question

y=23x+7
y=23x−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

Statement #1 is the correct approach for Mick to take.

To determine if two lines are parallel, you need to verify that they have the same slope but different y-intercepts. In this case, both equations are in slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

For the given lines:

1. \(y = 23x + 7\) has a slope of 23 and a y-intercept of 7.
2. \(y = 23x - 2\) also has a slope of 23 but a y-intercept of -2.

Since both lines have the same slope (23) but different y-intercepts (7 and -2), they are indeed parallel.

Therefore, the correct interpretation is represented by Statement #1: Mick should verify that the lines have the same slope but different y-intercepts.