Elizabeth A. answered • 12/03/19

Patient and Energetic Ivy League Math and Chemistry Tutor

First rearrange the equations into slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept.

Once in that form you can easily compare the slopes. As Paul M. states previously, the equations are parallel when they have the same slope.

So for the first equation:

y - 4 = 3(x + 5)

y - 4 = 3x + 15 (distribute the 3)

y = 3x + 19 (isolate y on left side of equation to get slope-intercept form y = mx + b)

Here you can see the slope is 3.

Rearrange the other 3 equations into the slope-intercept form, and you will see why Paul M. is correct.