4x +5y = -20
for an equation in standard form, you can write the equation for the perpendicular line by swapping the x- and y-coefficients and negating one of them. you need the x-coefficient to be positive, so it is needed to negate that one here. This gives you the equation ...
4x +5y = (some constant)
You find the value of the constant by evaluating the expression at the given point:
4x +5y = 4(5) +5(-8) = -20
The equation is 4x +5y = -20
