What is an equation of the line that passes through the point (5,-8) and is perpendicular to the line 5x- 4y= 16

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

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