What is the equation of the line that is perpendicular y=1/5x+4 and that passes through (5,-4) ?

The equation of the line that passes through (5, - 4)

and is perpendicular to line y = 1/5x + 4

is y = - 5x + 21

The slope that is perpendicular to the slope 1/5x is - 5x.

To find a perpendicular slope, you take the negative reciprocal.

The negative reciprocal of 1/5x is - 5/1x, or - 5x

However, y = - 5x + 4 does NOT pass through (5, - 4)

Looking at the line on a graph, we can find that if the y-intercept is 21, it DOES pass through (5, - 4)