Question

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 does not equal 0, what is the value of r/p?

A). 2/5
B). 3/4
C). 4/3
D). 5/2

Answer 1

Each point should satisfy the equation of the line it belongs to.
This means that:
for the equation of the first line (y=x+b), the point (p,r) satisfies this equation, thus: r = p + b ....................> equation I
for the equation of the second line (y=2x+b), the point (2p,5r) satisfies this equation, thus: 5r = 4p + b ...................> equation II
Subtract equation I from equation II to eliminate the constant b:
5r-r = 4p+b-p-b
4r = 3p
Thus, r/p = 3/4