Chapter 2 Linear Equations and Functions - 2.4 Write Equations of Lines - Guided Practice for Examples 4 and 5 - Page 100: 7

$y=x+5.$

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: $m=\frac{1-(-8)}{6-(-3)}=\frac{9}{9}=1.$ 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: $y-6=1(x-1)\\y-6=x-1\\y=x+5.$