The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (1, k) and (-1, -4) and the slope m = 3/2. Substitute:
[tex]\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}[/tex]
