Test 8 Section 4 #27 please

Yeah, this is a pretty tricky one! The key to getting through it is recognizing that whenever you have a point on a line, you can plug the coordinates into the line’s equation. Because the question wants to know about , we should start by getting our equations in terms of *r* and *p*.

We know (*p*, *r*) is on *y* = *x* + *b*, so we substitute:

Likewise, we know that (2*p*, 5*r*) is on *y* = 2*x* + *b*, so we substitute:

From there, we can use the fact that both equations have a *b* in them to our advantage. Solve each for *b*, then set them equal to each other:

Now just combine like terms and solve for :