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

Question

y = 2/3x + 7
y = 2/3x - 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 blank
describes the approach Mick should take based on the best reasoning.

Answer 1

The correct statement describing the approach Mick should take based on the best reasoning is:

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

This is because two lines are parallel if and only if they have the same slope (the coefficient of \(x\)) but different y-intercepts (the constant term). In this case, both lines have a slope of \( \frac{2}{3} \) but different y-intercepts (7 and -2), which confirms that the lines are indeed parallel.