Question

To write an equation of the line that is...

perpendicular to y= 2x - 3
and goes through the point (-4, 5)

Answer 1

`y = -(1)/(2) x + 3`

Explanation:

Perpendicular lines have a negative reciprocal gradient to the original line. This means you have to make the gradient negative and flip the original fraction.

The original gradient is 2 (which can be written 2/1), so the reciprocal is 1/2 and made negative it is -1/2.

Put this into the equation using form y = mx +c to get y = -1/2x + c.

To work out c, substitute the values of x and y given in the point:

5 = -1/2(-4) + c

5 = 2 + c

c = 3

Therefore, the equation for the perpendicular is:

`y = -(1)/(2) x + 3`