Question

What is the equation of a line that is perpendicular to y=5x-1 and passes through the point (2, -4)

Answer 1

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

Answer 2

y = -1/5x Hope this helps. I think this is the right answer.