Chapter 2 Linear Equations and Functions - 2.4 Write Equations of Lines - 2.4 Exercises - Skill Practice - Page 102: 35

$y=5x+23.$

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: $m=\frac{-2-8}{-5-(-3)}=\frac{-10}{-2}=5.$ 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: $y-8=5(x-(-3))\\y-8=5(x+3)\\y-8=5x+15\\y=5x+23.$