In this case the answer is very simple .
Step 01:
Data
equation of the given line: 5y = -3x -10
y = -3/5x - 2
m = -3/5
given point: (3,-6) x1 = 3 y1 = -6
Step 02:
Slope of the perpendicular line, m’
m' = (-1) / m
[tex]m\text{'}=\frac{-1}{-\frac{3}{5}}=\frac{5}{3}[/tex]Point-slope form of the line
(y - y1) = m (x - X1)
[tex](y\text{ - (-6)) = }\frac{5}{3}\cdot(x-3)\text{ }[/tex][tex]\begin{gathered} y\text{ +6=}\frac{5}{3}x\text{ -}\frac{5}{3} \\ y\text{ = }\frac{5}{3}x\text{ -}\frac{5}{3}-6 \\ \end{gathered}[/tex][tex]y\text{ = }\frac{5}{3}x\text{ -}\frac{23}{3}[/tex]The answer is:
The equation of the perpendicular line is:
y = (5/3) x - (23/3)
