Chapter 2 Linear Equations and Functions - 2.4 Write Equations of Lines - 2.4 Exercises - Skill Practice - Page 102: 45

$4x+3y=32.$

We know that by the Slope Formula: if $P_1(x_1,y_1)$ and $P_2(x_2,y_2)$ are on a line, then the slope is: $m=\frac{y_2-y_1}{x_2-x_1}$. Hence here: $m=\frac{8-16}{2-(-4)}=\frac{-8}{6}=\frac{-4}{3}.$ We know that if the slope of a line is $m$ and it contains $P_1(x_1,y_1)$, then its equation is: $y-y_1=m(x-x_1).$ Hence here: $y-8=\frac{-4}{3}(x-2)\\y-8=\frac{-4}{3}x+\frac{8}{3}\\3y-24=-4x+8\\4x+3y=32.$