Question

Find the equation of the line that passes through (-1,-3) and is perpendicular to

2y=x−3
Leave your answer in the form y=mx+c

Answer 1

y = -x/2 - 7/2

Explanation:

Equation of the line (current) in y = mx + c

• 2y = x - 3
• y = x/2 - 3/2

The slope of a perpendicular line has to be -ve to the current line.

⇒ m' = -1/2

To find the y-intercept, take the x-coordinate to be 0 and substitute in the equation :

y - y₁ = m (x - x₁)

y + 3 = -1/2 (0 + 1) [Also using the point (-1, -3) to make sure line crosses it]

y + 3 = -1/2

y = -7/2

Therefore, the new equation is :

• y = -x/2 - 7/2

Answer 2

y = -2x - 5

Explanation:

2y = x - 3

y = 1/2x - 3/2

gradient = 1/2

perpendicular gradient = negative reciprocal = -2

y = -2x + c

(-3) = -2(-1) + c

-3 = 2 + c

-5 = c