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2023-02-21

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

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

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