Caylee Villegas

2022-07-26

Write an equation of the line containing the given point and parallel to the given line.
$\left(9,-8\right);5x-2y=9$

Coleman Ali

Expert

The slope of the line $5x-2y=9$ is given by,
$2y=5x-9\phantom{\rule{0ex}{0ex}}y=\frac{5}{2}x-\frac{9}{2}\phantom{\rule{0ex}{0ex}}\text{Slope}=m=\frac{5}{2}$
The equation line passing through the point (9,-8) and parallel to $5x-2y=9$ is given by,
$y-{y}_{1}=m\left(x-{x}_{1}\right)\phantom{\rule{0ex}{0ex}}y-\left(-8\right)=\frac{5}{2}\left(x-9\right)\phantom{\rule{0ex}{0ex}}y+8=\frac{5}{2}x-\frac{45}{2}\phantom{\rule{0ex}{0ex}}y=\frac{5}{2}x-\frac{45}{2}-8\phantom{\rule{0ex}{0ex}}=\frac{5}{2}x-\frac{61}{2}$

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