Find an equation of the line that passes through the point (1/2, -2/3) and is perpendicular to the line 4x-8y=1.

Question

I really need help. None of the videos or text book examples are helping

Answer 1

Recall that the product of slopes of perpendicular lines is -1. Start by finding the slope of the given line.

4x - 8y = 1

-8y = -4x + 1

y = (1/2)x - 1/8

The slope of the given line is 1/2, so the slope of the perpendicular line is

m = -1/(1/2) = -2

The equation of the perpendicular line is

y = mx + b

y = -2x + b

Next, use the given point to find b.

-2/3 = -2(1/2) + b

Finally, solve for b, plug it into

y = -2x + b

and you are done. You should be able to finish from here.