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

Answer:

$y = 2x -4$

Step-by-step explanation:

$y = -\frac{1}{2}x - 2\ \ \ \ \ \ (0, -4)$

To find the perpendicular equation of a line,

You need the product of their gradients to be -1

$-\frac{1}{2} \times ? = -1$

Divide both sides by $-\frac{1}{2}$

? = 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...

$y = 2x -4$