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 = \(\frac{-1}{\frac{3}{2}} = \frac{-2}{3}\)

\(\implies \frac{y - (-3)}{x - 2} = \frac{-2}{3}\)

\(\frac{y + 3}{x - 2} = \frac{-2}{3} \)

\(3(y + 3) = -2(x - 2) \implies 3y + 2x + 9 - 4 = 0\)

= \(3y + 2x + 5 = 0\)

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