 # Find parametric equations for the line that passes through the Nefissi8u 2021-12-02 Answered
Find parametric equations for the line that passes through the point and is parallel to the line
$y=\frac{-7}{2}x-2$
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Step 1
The given equation of line
$y=\frac{-7}{2}x-2$
comaparing with the $y=mx+b$, we get
$m=\frac{-7}{2}$ and $b=-2$
The slope of the line is $\frac{-7}{2}$
Given that the line passes through the point is parallel to the line $y=\frac{-7}{2}x-2$
We know that the slope of parallel line is same
So, the line passes trough the point has slope $m=\frac{-7}{2}$
Step 2
$u\mathrm{sin}g$ point slope formula,
$y-{y}_{1}=m\left(x-{x}_{1}\right)$
Here
$⇒y-2=\frac{-7}{2}\left(x-5\right)$
$⇒\frac{y-2}{-7}=\frac{x-5}{2}=t\left(\le t\right)$
Now, $\frac{y-2}{-7}=t\phantom{\rule{0ex}{0ex}}⇒y-2=-7t\phantom{\rule{0ex}{0ex}}⇒y=2-7t$
and $\frac{x-5}{2}=t$
$⇒x=2t\phantom{\rule{0ex}{0ex}}⇒x=5+2t$
so, parametric equations for the line that passes through the point is