How to graph 3 x + 2 y = 2 by plotting points?

By first solving for ${\displaystyle y}$, change the standard equation for a line to the slope-intercept form. Slope-intercept form is ${\displaystyle y=mx+b}$, where ${\displaystyle m}$ is the slope and ${\displaystyle b}$ is the y-intercept.
${\displaystyle 3x+2y=2}$
Subtract ${\displaystyle 3x}$ from both sides.
${\displaystyle 2y=-2-3x}$
Divide both sides by ${\displaystyle 2}$.
${\displaystyle y=-\frac{2}{2}-\frac{3}{2}x}$
Simplify.
${\displaystyle y=1-\frac{2}{3}x}$
Rearrange into slope-intercept form.
${\displaystyle y=-\frac{2}{3}x+1}$
Now find two points on the line by choosing values for ${\displaystyle x}$ and solving for ${\displaystyle y}$.
${\displaystyle x=0,}$ ${\displaystyle y=1}$
${\displaystyle x=3,}$ ${\displaystyle y=-1}$
Plot the points on a graph and draw a straight line through the two points.
graph{y=-2/3x+1 [-10, 10, -5, 5]}