Question

what is an equation of the line that is perpendicular to line y= -1/2x -2 and passes through the point (0,-4)?

Answer 1

`y = 2x -4`

Explanation:

`y = -(1)/(2)x - 2\ \ \ \ \ \ (0, -4)`

To find the perpendicular equation of a line,

You need the product of their gradients to be -1

`-(1)/(2) * ? = -1`

Divide both sides by
`-(1)/(2)`

? = 2

The gradient of the perpendicular line is 2

Straight line formula is in the form
`y = mx + c`

`y = 2x + c`

We're nearly there, we just need to find out c.

Luckily, we're given a point
`(0, -4)`

`(x, y) = (0, -4)`

`y = 2x + c`

`-4 = 2(0) + c\\-4 = 0 + c\\c = -4`

We then end up with...

`y = 2x -4`