Calculate the slope of the line joining the points (1,1) and (-3,-1).
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{-1-1}{-3-1} \\ m=0.5 \end{gathered}[/tex]
Use the equation m1m2=-1 to calculate the slope of the perpendicular line.
[tex]\begin{gathered} m1m2=-1 \\ m2=-\frac{1}{m1} \\ m2=-\frac{1}{0.5} \\ m2=-2 \end{gathered}[/tex]
Given that, the line passes through the point (-3,4).
Use point slope form to calculate the equation of the line.
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-4=-2(x+3) \\ y-4=-2x-6 \\ y=-2x-2 \end{gathered}[/tex]
Therefore, the equation of the line is y=-2x-2.
