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
r
p
?

A)
2
5

B)
3
4

C)
4
3

D)
5
2

Answer 1

Answer:

(D) 52

Step-by-step explanation:

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Answer 2

Answer:

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

.

Step-by-step explanation: