Question

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

The correct statement that describes the approach Mick should take is Statement #1: "Mick says he should verify that the lines have the same slope but different y-intercepts."

This is because parallel lines have the same slope, which means they will rise or fall at the same rate, but they will not intersect, so they must have different y-intercepts. In the given equations:

- For \( y = 23x + 7 \), the slope is 23 and the y-intercept is 7.
- For \( y = 23x - 2 \), the slope is also 23 but the y-intercept is -2.

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