Question

Find the equation of a line drawn perpendicular to the line x/4 + y/6 = 1 through the point, where it meets the y-axis.

Answer 1

Given equation x/4 + y/6 = 1 is in intercept form

∴ Point on the y-axis is (0, 6)

Now, slope of the given line = - (1/4)/(1/6) = - 3/2

∴ Slope of any line perpendicular to given line

= 2/3 ∵ m₁ x m₂ = - 1

∴ Required equation of the line through (0, 6) and perpendicular to given line is

y - 6 = 2/3(x - 0) ⇒ 2x - 3y + 18 = 0