Question

Solve for k if the line through the two given points is to have the given slope

Answer 1

Step 1

Given;

$\begin{gathered} m=\frac{2}{3} \\ (2,4) \\ (4,k) \end{gathered}$

Step 2

Using the point-slope formula

$\begin{gathered} y-y_1=m\frac{}{}(x-x_1) \\ y-4=\frac{2}{3}(x-2) \\ y-4=\frac{2}{3}(x-2) \\ y=k \\ x=4 \\ k-4=\frac{2}{3}(4-2) \\ k-4=\frac{2}{3}(2) \\ k-4=\frac{4}{3} \\ k=\frac{4}{3}+4 \\ k=\frac{16}{3} \end{gathered}$

Answer; Op B

$k=\frac{16}{3}$