Question

Find the equation of a line, which is perpendicular to the line 2x − 4y + 12 = 0 and has a y-intercept of −3 units.

Answer 1

⇒ Rewriting the given equation 2x − 4y + 12 = 0 into the slope-intercept form, y = mx + c to find the slope (m₁):

−4y = −2x − 12

y = `(-2)/-4 x - 12/-4`

`y = 1/2 x + 3`

∴ The slope (m₁) of the given line is `1/2`.

⇒ For perpendicular lines, the product of their slopes is −1. Let’s find slope (m₂):

m₁ × m₂ = −1

`(1/2) xx m_2 = -1`

m₂ = −2

⇒ We are given that the y-intercept (c) is −3, so using the slope-intercept form y = mx + c:

y = −2x + (−3)

y = −2x − 3

⇒ Rearranging the above equation in the standard form (Ax + By + C = 0),

2x + y + 3 = 0

Hence, the equation of the line is 2x + y + 3 = 0.