Slope intercept form: y = mx + b
m = slope and b = y-intercept
From y = 5x - 1 we can already see that the slope is 5 since it is already in slope intercept form.
The slope of the perpendicular line is the negative reciprocal of the slope for the equation y = 5x - 1.
The negative reciprocal of 5 is -1/5.
So the incomplete equation for the perpendicular line is y = -1/5(x) + b
To find b plug in the x and y values from (2,-4) into the equation to get
-4 = -1/5(2) + b
b = -4 + 1/5(2)
b = -4 + 2/5
b = -18/5
The equation of the perpendicular line is y = -1/5(x) -18/5