Question

Find the line perpendicular to y=-1/2x-1 that includes the point (-2,4).

Answer 1

Answer: y = 2x + 8

Step-by-step explanation

The given line is y = (-1/2)x - 1

Compare it to y = mx+b to see that m = -1/2 is the original slope.

Flip the fraction and flip the sign to get the perpendicular slope 2.

In other words, the negative reciprocal of -1/2 is 2.

Then apply point-slope form to determine the perpendicular equation.

`y - y_1 = m(x - x_1)\\\\y - 4 = 2(x - (-2))\\\\y - 4 = 2(x + 2)\\\\y = 2(x + 2) + 4\\\\y = 2x + 4 + 4\\\\y = 2x + 8\\\\`

As a check, let's plug in the coordinates of (-2,4).

y = 2x+8

4 = 2(-2)+8

4 = -4+8

4 = 4

We get the same thing on both sides, so we have confirmed the answer is correct.