Use the Rectangular Coordinate System: example 4.8

We can substitute any value we want for $x$ or any value for $y$. Since the equation is in y-form, it will be easier to substitute in values of $x$. Let’s pick $x=0$, $x=1$, and $x=\mathrm{-1}$.

Substitute the value into the equation.
Simplify.
Simplify.
Write the ordered pair.			(0, 2)	(1, −1)	(−1, 5)
Check.
$y=\mathrm{-3}x+2$	$y=\mathrm{-3}x+2$	$y=\mathrm{-3}x+2$
$2\stackrel{?}{=}\mathrm{-3}\cdot 0+2$	$\mathrm{-1}\stackrel{?}{=}\mathrm{-3}\cdot 1+2$	$5\stackrel{?}{=}\mathrm{-3}\left(\mathrm{-1}\right)+2$
$2\stackrel{?}{=}0+2$	$\mathrm{-1}\stackrel{?}{=}\mathrm{-3}+2$	$5\stackrel{?}{=}3+2$
$2=2✓$	$\mathrm{-1}=\mathrm{-1}✓$	$5=5✓$

So, $\left(0,2\right)$, $\left(1,\mathrm{-1}\right)$ and $\left(\mathrm{-1},5\right)$ are all solutions to $y=\mathrm{-3}x+2$. We show them in Table 4.8.