Two lines are perpendicular if the product of their slopes is -1. In this example, the slope of one of the slopes is -5/3 (the coefficient of the x variable when the equation is solved for y), then the slope of the new line must satisfy
[tex]\begin{gathered} -\frac{5}{3}m=-1 \\ m=\frac{3}{5} \end{gathered}[/tex]
Using the point-slope form, we have
[tex]\begin{gathered} y-(-1)=\frac{3}{5}(x-(-5)) \\ y+1=\frac{3}{5}x+3 \\ y=\frac{3}{5}x+2 \end{gathered}[/tex]
Then, the slope-intercept form of the equation is
[tex]y=\frac{3}{5}x+2[/tex]
