In order to find the equation, let's use the slope-intercept form of the linear equation:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Using the points (-4, -5) and (6, 1), we can calculate the values of m and b:
[tex]\begin{gathered} (-4,-5)\colon \\ -5=-4m+b\to b=4m-5 \\ \\ (6,1)\colon \\ 1=6m+b \\ 1=6m+4m-5 \\ 10m-5=1 \\ 10m=1+5 \\ 10m=6 \\ m=\frac{6}{10}=\frac{3}{5} \\ \\ b=4\cdot(\frac{3}{5})-5=\frac{12}{5}-\frac{25}{5}=\frac{-13}{5} \\ \\ y=\frac{3}{5}x-\frac{13}{5} \end{gathered}[/tex]