Question

Find the equation of the line that passes through (-1,2) and is perpendicular to 2y=x−3.

Leave your answer in the form y=mx+c

Answer 1

y = -2x.

Explanation:

2y = x - 3

y = 1/2x - 3/2

- so, the slope of this line is 1/2

and the slope of a line perpendicular to it is - 1/ 1/2

= -2.

Using the point slope form of a line the equation of the required line is

y - y1 = m(x - x1)

m = -2, x1 = -1 and y1 = 2.

So,

y - 2 = -2(x - (-1))

y - 2 = -2x - 2

y = -2x - 2 + 2

y = -2x.

Answer 2

2y = x - 3
y = 1/2x - 1.5
If a line is perpendicular to another line, its gradient is the negative reciprocal of the first line.
y = -2x + c
2 = -2 x - 1 + 0
y = -2x