Chapter 4 - Writing Linear Functions - 4.2 - Writing Equations in Point-Slope Form - Monitoring Progress - Page 183: 4

$ y=-\frac{1}{4}x-2$

Let $(x_{1},y_{1})=(-4,-1)$ and $(x_{2},y_{2})=(8,-4)$ Slope $m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-4-(-1)}{8-(-4)}=\frac{-3}{12}=-\frac{1}{4}$ Point-slope form is $y-y_{1}=m(x-x_{1})$ Substituting the values, we get $y-(-1)=-\frac{1}{4}(x-(-4))$ $\implies y+1=-\frac{1}{4}(x+4)$ $\implies y+1=-\frac{1}{4}x-1$ $\implies y=-\frac{1}{4}x-2$ The equation of line is $ y=-\frac{1}{4}x-2$