Marco is trying to determine whether the following two lines are parallel. y=2/3x+7 y=2/3x−5 Which statement correctly describes the approach Marco should take based on the best reasoning? Statement #1: Marco says he should verify that the lines have the same slope but different y-intercepts. Statement #2: Marco says he should verify that the lines have the same y-intercept but different slopes

Answer 1

To determine whether two lines are parallel, Marco should focus on their slopes. Parallel lines have the same slope but different y-intercepts.

In this case, both lines are given in slope-intercept form (y = mx + b), where \( m \) is the slope and \( b \) is the y-intercept.

The two lines are:

1. \( y = \frac{2}{3}x + 7 \) (slope = \( \frac{2}{3} \), y-intercept = 7)
2. \( y = \frac{2}{3}x - 5 \) (slope = \( \frac{2}{3} \), y-intercept = -5)

Since both lines have the same slope of \( \frac{2}{3} \) but different y-intercepts (7 and -5), they are indeed parallel.

Thus, the correct approach Marco should take is described by Statement #1: "Marco says he should verify that the lines have the same slope but different y-intercepts."