Help me prove this math problem true - slopes

Suppose the slope of a straight line L is -3/4 and P is a given point on L. If Q is a point on L lying 2 units to the right of P, then Q is situated 3/2 units below P.

The line L has an equation y = -¾ x + c. The value of c doesn't matter for this question, so let c = 0.

Hence, if P is the point (p, q) and Q is the point (s, t),

q = -¾p, and t = -¾s,


But Q is 2 units to the right of P, therefore its x-coordinate = (p + 2)

So in the equation t = -¾s, we can substitute (p + 2) for s, giving

t = -¾(p + 2)

. = -¾p - ¾ (2)

and since q = -¾p, then

t = q - (3/2)

So the y-coordinate of Q is (3/2) units below the y-coordinate of P.

slope is y2-y1/x2-x1=-3/2.since the difference of y coordinates gives the height of line.

- 3/4 = (y2-y1) / (x2-x1)
if x2-x1 = 2
then y2-y1 =

-3/4 = (y2-y1) /2
- 6/4 = y2-y1 = -3/2
indeed the rise = 3/2