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


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Answer 1

Step-by-step explanation:

In the xy-plane, the point (p, r) lies on the line with equation y = x + b, where b is a constant and the point with coordinates (2p, 5r) lies on the line with equation y = 2x + b.

Answer 2

Answer:-

• rp = 3/4

Explaination:-

→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

rp

, 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

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