Question

What is the equation of the line which is perpendicular to `2x+y=-4` which passes through the point `(2,-8)?`

Answer 1

`y = 1/2x - 9`

Explanation:

Given equation : `2x + y = - 4`

We rewrite this in Slope-Intercept form, that is;

`y = -2x - 4`

The slope in this equation's case is `m = -2`

Therefore, the slope of a line that is perpendicular to this line is going to be the negative reciprocal of the given slope.

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

The y-intercept can be determined from the coordinates provided.
`(2,-8).`

Substitute the values of the x and y coordinate in its Slope-Intercept form to determine the `y`-intercept:

`y = mx + b`
`-8 = (1/2)(2) + b`
`b = -9`

Therefore, the equation of the line is `y = 1/2x - 9`