# Find parametric equation of the line passing through point (4,\

Find parametric equation of the line passing through point parallel to vector
$\stackrel{\to }{v}=-\stackrel{^}{i}+5\stackrel{^}{j}$
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Step 1
Given:
A line passes through the point
The line is parallel to the direction vector $\stackrel{\to }{v}=-\stackrel{^}{i}+5\stackrel{^}{j}$
We want to find the parametric equations of the line passing through and parallel to the vector
$\stackrel{\to }{v}=-\stackrel{^}{i}+5\stackrel{^}{j}$
The parametric equations for a line though the point and parallel to direction vector is given by
$x={x}_{0}+at$ and $y={y}_{0}+bt$
Step 2
In the given problem, we have and
Since and a in the parametric equation.
Hence
$x={x}_{0}+at$
$⇒x=4+\left(-1\right)t$
$⇒x=4-t$
Now and b in the parametric equation.
Hence
$y={y}_{0}+bt$
$⇒y=2+\left(5\right)t$

$⇒y=2+5t$
Hence $x=4-t$ and $y=2+5t$ are parametric equations for the line passing through the point and parallel to the vector $\stackrel{\to }{v}=-\stackrel{^}{i}+5\stackrel{^}{j}$