Mick is trying to determine whether the following two lines are parallel or not. y=23x+7y=23x+7 y=23x−2y=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 slopes but different y-intercepts. Statement #2: Mick says he should verify that the lines have the same y-intercepts but different slopes. (1 point) Statement # describes the approach Mick should take based on the best reasoning.

Answer 1

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

Given the two equations:

1. \( y = 23x + 7 \)
2. \( y = 23x - 2 \)

Both lines have the same slope of 23, but different y-intercepts (7 and -2 respectively).

Therefore, the correct approach based on the best reasoning is:

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

This statement is correct because it accurately describes the condition for the lines to be parallel.