Question

find the perpendicular distance between y=2x+2 and y=2x+7

Answer 1

Well, as you can see, the slope of both of these is \(\sf \color{red}{2}\), which means the perpendicular is \(\sf \color{red}{-\frac{1}{2}}\).
That means, get "x" and "y" points.

the intersection with the first line is where \(\sf \color{blue}{-\frac{1}{2} x + 2 = 2x + 7}\)
x = -2
then y = 2(-2)+7 = 3

So your first point is (-2,3).
Now, can you find your second? You can pick any point on the line.

Then use distance formula to get the distance.