Question

Find the value of k so that the line through the given points has the given slope.

Answer 1

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (1, k) and (-1, -4) and the slope m = 3/2. Substitute:

$\dfrac{-4-k}{-1-1}=\dfrac{3}{2}\\\\\dfrac{-4-k}{-2}=\dfrac{3}{2}\qquad\text{multiply both sides by (-2)}\\\\-4-k=-3\qquad\text{add 4 to both sides}\\\\-k=1\qquad\text{change the signs}\\\\\boxed{k=-1}$