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 \dfrac{r}{p}, we should start by getting our equations in terms of r and p.

We know (pr) is on yxb, so we substitute:


Likewise, we know that (2p, 5r) is on y = 2xb, 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 \dfrac{r}{p}:



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