Question

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

Answer 1

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

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:

`3x-2y=6`
`3(0)-2y=6`
`-2y=6`
`y=-3`

So that's one point `(0,-3)`

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

`3x-2y=6`
`3x-2(0)=6`
`3x=6`
`x=2`

And that's our other point `(2,0)`

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