Answer:
The answer is that r = -6.
Step-by-step explanation:
Given points (5, r) and (3, -2) with a slope of -2, solve for r.
Solve using the Point slope form to obtain a function:
(y1 - y) = m(x1 - x)
Use point (3, -2):
(-2 - y) = -2(3 - x)
-2 - y = -6 + 2x
-y = +2 - 6 + 2x
-y = -4 + 2x
y = -2x + 4
As a function:
f(x) = -2x + 4
f(5) = -2(5) + 4 = -10 + 4 = -6.
Solve using another method:
(y1 - y) / (x1 - x) = m
Let x = 5, y = r and x1 = 3 and y1 = -2, and then substitute:
(-2 - r) / (3 - 5) = m
-2 - r = m(3 - 5)
-2 - r = 3m - 5m, substitute -2 for m
-2 - r = 3(-2) - 5(-2)
-2 - r = -6 + 10
-2 - r = 4
-r = 6
r = -6
