Find the equation of the straight line that passes through (2, -3) and perpendicular to the line 3x – 2y + 4 = 0.
-
A.
2y – 3x = 0 -
B.
3y – 2x + 5 = 0 -
C.
3y + 2x + 5 = 0 -
D.
2y – 3x – 5 = 0
Correct Answer: Option C
Explanation
Given line: (3x – 2y + 4 = 0 implies 2y = 3x + 4)
(y = frac{3}{2}x + 2)
(Gradient (frac{mathrm d y}{mathrm d x}) = frac{3}{2})
Gradient of perpendicular line = (frac{-1}{frac{3}{2}} = frac{-2}{3})
(implies frac{y – (-3)}{x – 2} = frac{-2}{3})
(frac{y + 3}{x – 2} = frac{-2}{3} )
(3(y + 3) = -2(x – 2) implies 3y + 2x + 9 – 4 = 0)
= (3y + 2x + 5 = 0)