In the xy-plane, the point (p, r) lies on the line with equation y=x+b, where b is a constant. The point with coordinates (2p,5r) lies on the line with equation y=2x+b. If p≠0, what is the value of r/p?

A) 2/5

B) 3/4

C) 4/3

D) 5/2

B

Explanation:

If the point (p, r) lies on y = x + b, then if we plug in p for x and r for y, the equation will hold true. So let's try that:

r = p + b

Now, since the point (2p, 5r) lies on the line y = 2x + b, we can plug 2p in for x and 5r in for y:

5r = 2 * 2p + b

5r = 4p + b

Let's substitute p + b in for r:

5r = 4p + b

5 * (p + b) = 4p + b

5p + 5b = 4p + b

p = -4b

We now have p in terms of b. Let's do the same for r, so plug -4b in for p in

r = p + b:

r = p + b

r = -4b + b

r = -3b

We want to find the value of r/p, so let's right this in terms of b:

r/p

-3b/-4b

The b's and negative signs will cancel out, so we're left with 3/4.

The answer is B.

Hope this helps!