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?​

Answer 1

Answer:

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Answer 2

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 = rp.

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 3

4