Find the equation of the straight line perpendicular to 2x – 3y = 5 and cutting off an intercept 1 on the positive direction of the x-axis.
Given: equation is perpendicular to 2x − 3y = 5 and cutting off an intercept 1 on the positive direction of the x-axis.
Explanation:
The line perpendicular to 2x − 3y = 5 is
3x + 2y + λ = 0
It is given that the line 3x + 2y + λ = 0 cuts off an intercept of 1 on the positive direction of the x axis.
This means that the line 3x + 2y + λ = 0 passes through the point (1, 0).
∴ 3 + 0 + λ = 0
⇒ λ = -3
Substituting the value of λ, we get 3x + 2y – 3 = 0,
Hence, equation of the required line.