Question

Write an equation for a line perpendicular to y = 5 x − 4 y=5x-4 and passing through the point (-15,0)

Answer 1

Use point -slope form of equation of line:
$y - y_0 = m(x-x_0) \\ \\ (x_0,y_0) = (-15,0) \\ \\ y = m(x+15)$

Next determine perpendicular slope.
Slope of given line is 5.
Perpendicular slopes must multiply to -1.
---> 5m = -1
---> m = -1/5

Sub into line equation for 'm'.
$y = -\frac{1}{5} (x+15) \\ \\ y = -\frac{1}{5} x - 3$