Question

Use slopes and y-intercepts to determine if the lines 15x−15y=−4 and −5x + 5y=−3 are parallel.

Select the correct answer below:
a. parallel
b. not parallel

Answer 1

After converting both equations into slope-intercept form, it is revealed that they both have the same slope but different y-intercepts. Therefore, the lines are parallel.

Step-by-step explanation:

To determine if the lines 15x - 15y = -4 and -5x + 5y = -3 are parallel, we need to compare their slopes. First, we'll rewrite each equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

For the first equation, 15x - 15y = -4, we get:

y = x + ⅓

This means the slope (m) of the first line is 1.

For the second equation, -5x + 5y = -3, we simplify to:

y = x - ⅓

The slope (m) of the second line is also 1.

Since both lines have the same slope, we can conclude that the lines are indeed parallel.