NCERT · Class 11 · Mathematics · Straight LinesFind the equation of the line passing through the point $(-1, 1)$ and parallel to the line $2x - 3y + 4 = 0$.
The slope of the line $2x - 3y + 4 = 0$ is $m = -\frac{2}{-3} = \frac{2}{3}$. A parallel line has the same slope, so $m = \frac{2}{3}$. Using the point-slope form with point $(-1, 1)$: $y - 1 = \frac{2}{3}(x - (-1)) \implies 3(y - 1) = 2(x + 1) \implies 3y - 3 = 2x + 2 \implies 2x - 3y + 5 = 0$. Therefore, the correct option is C.
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Straight Lines.
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Straight Lines.
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Straight Lines.