To find the equation, first, we have to find the slope.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let's replace the points (-4,-7) and (2,-4).
[tex]m=\frac{-4-(-7)}{2-(-4)}=\frac{-4+7}{2+4}=\frac{3}{6}=\frac{1}{2}[/tex]
Then, we use the point-slope equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-4)=\frac{1}{2}(x-2) \\ y+4=\frac{1}{2}x-1 \\ y=\frac{1}{2}x-1-4 \\ y=\frac{1}{2}x-5 \end{gathered}[/tex]
Hence, the equation is
[tex]y=\frac{1}{2}x-5[/tex]
