Question

Use slopes and y-intercepts to determine if the lines 9x - 2y = 5 and 3x - y = 1 are parallel.

Select the correct answer below:
Parallel
Not Parallel

Answer 1

To determine if two lines are parallel, compare their slopes. The lines 9x - 2y = 5 and 3x - y = 1 are not parallel.

Step-by-step explanation:

To determine if two lines are parallel, we can compare their slopes. The given lines 9x - 2y = 5 and 3x - y = 1 can be rewritten in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

For the first equation, by rearranging it, we get -2y = -9x + 5, and dividing by -2 gives y = 9/2x - 5/2. Therefore, the slope is 9/2.

For the second equation, by rearranging it, we get -y = -3x + 1, and dividing by -1 gives y = 3x - 1. Therefore, the slope is 3.

Since the slopes of the two lines are not equal (9/2 ≠ 3), we can conclude that the lines 9x - 2y = 5 and 3x - y = 1 are not parallel.

Learn more about Determining parallel lines