Question

What is an equation of the line that is perpendicular to y – 4 = 2(x – 6) and passes through the point (–3, –5)?

Comments

the correct answer is y+5=-1/2(x+3)

Answer 1

The gradient of the given line is 2 (coefficient of x), so the gradient of the perpendicular is -½.

The equation of the perpendicular is y=-½x+a. To find a we plug in the given point:

-5=+3/2+a, so a=-5-3/2=-13/2 and y=-½(x+13).

Another way to write this is in the form y-Y=-½(x-X) where (X,Y)=(-3,-5) the given point.

So y+5=-½(x+3), which is equivalent to y=-½(x+13).