First, let's calculate the slope:
[tex]\begin{gathered} m=\frac{-6-10}{1-(-3)}\rightarrow m=\frac{-16}{1+3}\rightarrow m=\frac{-16}{4} \\ \rightarrow m=-4 \end{gathered}[/tex]Using this, point (1, -6) and the slope-point form, we get that the equation is:
[tex]\begin{gathered} y-(-6)=-4(x-1) \\ \rightarrow y+6=-4x+4 \\ \rightarrow y=-4x-2 \end{gathered}[/tex]Thereby, the equation of the line is
[tex]y=-4x-2[/tex]