The points (5,r) and (3,−2) lie on a line with a slope of −2 . what is the value of r ?

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

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