Find the equation of the line passing through the point $(-1, 1)$ and parallel to the line $2x - 3y + 4 = 0$.
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Question

Find the equation of the line passing through the point $(-1, 1)$ and parallel to the line $2x - 3y + 4 = 0$.

Accepted Answer

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.

Straight Lines

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