How do you graph 3x - 2y = 6 by plotting intercepts?

Solve for the intercepts and find your two intercept points of y-intercept = $\left(0 , - 3\right)$ and x-intercept = $\left(2 , 0\right)$

Explanation:

When we plot a graph using intercepts, we are being given 2 points: (0,?) and (?,0) - I'm using the very un-math-like ? to take away a little formality here! We substitute in the two points (or as much as we know about each point), then solve for the other part.

Let's do the y-intercept first. We know that where the graph passes through the y axis, $x = 0$ (we don't move right or left from the origin to find the y axis, so $x = 0$). So with $x = 0$, let's solve for y and find our first point:

$3 x - 2 y = 6$
$3 \left(0\right) - 2 y = 6$
$- 2 y = 6$
$y = - 3$

So that's one point $\left(0 , - 3\right)$

Let's do the x intercept. Following the same reasoning as before, we know that $y = 0$ so let's solve for x:

$3 x - 2 y = 6$
$3 x - 2 \left(0\right) = 6$
$3 x = 6$
$x = 2$

And that's our other point $\left(2 , 0\right)$

Plot those 2 points, connect them with a straight edge, and you'll get your graph.