Answer:
[tex]y=\frac{1}{3}x-\frac{16}{3}[/tex]
Step-by-step explanation:
Arranging the given equation in slope-intercept form ( y = mx + b ):
[tex]y+1=-3(x-5)\\y+1=-3x+15\\y=-3x+15-1\\y=-3x+14[/tex]
We know that the perpendicular line would have a slope (m) that is negative reciprocal of this ([tex]\frac{1}{3}[/tex]). Thus we can write the perpendicular line's equation as [tex]y=\frac{1}{3}x+b[/tex].
Now putting x = 4 and y = -6 into the equation, we can solve for b:
[tex]y=\frac{1}{3}x+b\\-6=\frac{1}{3}(4)+b\\-6=\frac{4}{3}+b\\b=-6-\frac{4}{3}\\b=-\frac{16}{3}[/tex]
Thus, the equation of the perpendicular line is [tex]y=\frac{1}{3}x-\frac{16}{3}[/tex]
