Question

What is the equation of the line that is perpendicular to 2x + 4y = 1 and that passes through the point (6, 8)?

Answer 1

`y = 2x - 4`

Explanation:

Step 1) Solve for `y` in order to find the slope of the line in the equation given:

`2x + 4y = 1`

`2x - 2x + 4y = 1 - 2x`

`0 + 4y = -2x + 1`

`4y = -2x + 1`

`(4y)/4 = (-2x)/4 + 1/4`

`y = -1/2x + 1/4`

Therefore the slope is `-1/2` and the slope of the perpendicular line is the flipped and negative of this: `- -2/1 -> +2 -> 2`

Step 2) Use the point slope for to obtain the equation for the perpendicular line:

`y - 8 = 2(x - 6)`

`y - 8 = 2x - 12`

`y - 8 + 8 = 2x - 12 + 8`

`y - 0 = 2x - 4`

`y = 2x - 4`