We need to determine the equation of the line in point-slope form, which is given below:
[tex]y-y_0=m\cdot(x-x_0)[/tex]Where (x0, y0) is a known point, and m is the slope of the line. In order to determine the slope, we can use the following expression:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1, y1) and (x2, y2) are two known points on the line. For our case they are (5, -6) and (-1, 6). Therefore, we have:
[tex]\begin{gathered} m=\frac{6-(-6)}{-1-5} \\ m=\frac{6+6}{-6} \\ m=\frac{12}{-6}=-2 \end{gathered}[/tex]The slope is -2. Now we can determine the equation:
[tex]y-6=-2\cdot(x+1)[/tex]