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

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Solution

Given equation line, $3 x - 4 y + 2 = 0$
$∴ 4 y = 3 x + 2$
$y = (\frac{3}{4}) x + \frac{1}{2}$
Slope of given line $= \frac{3}{4}$
As slope of parallel lines are equal
$∴$ Slope of line parallel to given line $= \frac{3}{4}$
Equations of line passes through $(- 2, 3)$ with slope $(\frac{3}{4})$ is
$(y - 3) = \frac{3}{4} (x + 2)$
$4 y - 12 = 3 x + 6$
$3 x - 4 y + 18 = 0$ be the equation of line parallel to $3 x - 4 y + 2 = 0$ and passing through $(- 2, 3)$

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