Let d be the (shortest) distance between 2 parallel lines with slope 6 whose -intercepts are 8 units apart. find d^2.

First you have to draw the both lines, like I did

Now you have to imagine that the shortest distance is a perpendicular line (C) like in my drawing.

Using the trigonometrical properties we can find the angle



then we can use the trigonometrical property of sine







____________________________________________________

Another way to solve this question:

You have to find the line equations







you can chose equation 1 or equation 2, but be careful, the point should be (0,8) if you pick up the equation 1 and the point should be (0,0) if you pick up the equation 2, I prefere to use the first one





replacing the point (0,8)