# A graph of a linear equation passes through ( -2,0) & (0,-6) is the 3x-y=6, both ordered pairs solutions for the equation

A graph of a linear equation passes through ( -2,0) and (0,-6) is the $3x-y=6$, both ordered pairs solutions for the equation

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$3x-y=6$ (1)
We know that the equatioan passing through $\left({x}_{1},{y}_{1}\right)and\left({x}_{2},{y}_{2}\right)$ is
$y-{y}_{1}=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\left(x-{x}_{1}\right)$
$y-0=\frac{-6-0}{0-\left(-2\right)}\left(x-\left(-2\right)\right)$
$y=-\frac{6}{2}\left(x+2\right)$
$y=-3\left(x+2\right)$
$y=-3x-6$
$3x+y+6=0$
$3x+y=-6\left(2\right)$
By, equations $\left(1\right)+\left(2\right)$, we get
$3x-y=6$
$3x+y=-6$
$6x=0⇒x=0$
put value in equation (2), we get
$3x+y=-6$
$3×0+y=-6$
$y=-6$
So, ordered parts (0,-6)