The line parallel to $4 x + 3 y + 7 = 0$ and passing through $(2, 1)$ is ____

4 x + 3 y + 11 = 0

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4 x + 3 y + 8 = 0

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4 x + 3 y - 8 = 0

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4 x + 3 y - 11 = 0

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Solution

The correct option is D $4 x + 3 y - 11 = 0$
Two parallel lines have the same slope, put $4 x + 3 y = - 7$ in slope-intercept form:
$4 x + 3 y = - 7$
$3 y = - 4 x - 7$
$y = - \frac{4}{3} x - \frac{7}{3}$
The slope is $- \frac{4}{3}$ , so a line parallel to this has a slope of $- \frac{4}{3}$ also.
Now since the equation of a line is $y - y_{1} = m (x - x_{1})$ where $m$ is the slope of the line.
Therefore with point $(2, 1)$ we have:
$(y - 1) = - \frac{4}{3} (x - 2) \Rightarrow 3 (y - 1) = - 4 (x - 2) \Rightarrow 3 y - 3 = - 4 x + 8 \Rightarrow 4 x + 3 y - 8 - 3 = 0 \Rightarrow 4 x + 3 y - 11 = 0$
Hence, resulting linear equation is $4 x + 3 y - 11 = 0$ .

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