Put the given line in Slope Intercept Form by solving it for y
Use the known relationship between the slopes of perpendicular lines they have inverse slopes of opposite signs.
Plug the points into the Slope Intercept Form of Perpendicular line to solve for b
First the given line
3x - 5y = 6
-5y = -3x + 6
Divide both sides by negative 5
y = (-3/-5)x - 6/5
y = (3/5)x - 6/5
In Slope Intercept Form is
y = (3/5)x - 6/5
so m = (3/5)
The slope of the Perpendicular would be negative inverse of 3/5 or
m = (-5/3)x
The Slope Intercept form for the perpendicular line is
y = (-5/3)x + b
Use the coordinates (-8,0) to solve for b
0 = (-5/3)(-8) + b
0 = 40/3 + b
Subtract 40/3 from both sides of the equation
-40/3 = b
The perpendicular line is
y = (-5/3)x - 40/3
