Question

In the xy-plane, the point (p,r) lies on the line with equation y=x+b, where b is constant. The point with coordinates (2p, 5r) lies on the line with equation y=2x+b. If p is not 0 what is the value of p/r

Answer 1

4/3

Step-by-step explanation:

For xy-plane coordinates, points are written as (x, y).

This question gives us two points and two line equations to solve this. Let's start with the first one.

Since p is the x value of the point and r is the y value of the point, we can place these values in our equation y = x + b as follows:

r = p + b

Now we do the same with our second point and line equation. We will substitute 2p for x and 5r for y in the equation y = 2x + b. So we get this:

5r = 2(2p) + b

5r = 4p + b

Since we have this two equations with the same two variables, now we can solve them using the elimination method.

In this case I eliminated b as it is constant in both equations. To do this I subtract the equations in order to cancel the b variable.

5r = 4p + b

r = p + b

_______ -

5r - r = 4p + b - p - b

4r = 3p

4/3 = p/r