First, let's take a look at the point-slope form of a line:
[tex]y-y_0=m(x-x_0)[/tex]Where:
• m, is the ,slope, of the line
,• (Xo,Yo) ,is a point that belongs to the line
Now, let's calculate the slope of our line with the poins given:
[tex]\begin{gathered} m=\frac{6-(-6)}{-1-5}\rightarrow m=\frac{6+6}{-6}\rightarrow m=\frac{12}{-6} \\ \\ \rightarrow m=-2 \end{gathered}[/tex]Using this slope and point (5,-6), we'll get the equation of our line in the point-slope form.
[tex]y-y_0=m(x-x_0)\rightarrow y-(-6)=-2(x-5)\rightarrow y+6=-2(x-5)[/tex]The equation of the line is the following:
[tex]y+6=-2(x-5)[/tex]