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

Question

y = 2x + 7
y=j2- 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 the slope of each line. Two lines are parallel if they have the same slope and different y-intercepts.

Let’s analyze the given equations:

1. The first line is in slope-intercept form \(y = 2x + 7\), where the slope is \(2\).
2. The second line is given as \(y = j2 - 5\). It appears that there might be a typo, and it should likely represent another linear equation. Assuming it meant \(y = 2x - 5\), then the slope is also \(2\).

Since both lines have the slope of \(2\) but different y-intercepts (\(7\) for the first line and \(-5\) for the second line), they are parallel.

Thus, the correct reasoning would be:

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

This statement is correct for determining whether the lines are parallel.