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≠0, what is the value of rp?

A) 2/5

B) 3/4

C) 4/3

D) 5/2​

Answer 1

Step-by-step explanation:

ANSWER EXPLANATION:

Since the point (p,r) lies on the line with equation y=x+b, the point must satisfy the equation. Substituting p for x and r for y in the equation y=x+b gives r=p+b, or b = r−p.

Similarly, since the point (2p,5r) lies on the line with the equation y=2x+b, the point must satisfy the equation. Substituting 2p for x and 5r for y in the equation y=2x+b gives:

5r=2(2p)+b

5r=4p+b

b = 5r−4p.

Next,

we can set the two equations equal to b equal to each other and simplify:

b=r−p=5r−4p

3p=4r

Finally, to find

r/p

we need to divide both sides of the equation by p and by 4

3p=4r

3=4r/p

3/4=r/p

The correct answer is B.3/4 (Ans)

Answer 2

Answer:

b) 3/4

hope it's help you ✌️✌️