Question

How do you graph `3x-y=9` using intercepts?

Answer 1

Get the y-intercept and x-intercept, then draw a continuous and linear line across the y and x-intercept.

Explanation:

We are able to draw a linear line across the y-intercept and x-intercept because we know it's a linear line a.k.a. the slope never changes.

So since we know this, we should firstly isolate the y. First we subtract `3x` from both sides so we get something like `-y=-3x+9`.

Now to fully isolate y, we divide both sides by -1 (or multiply). If we do we get something like `y=3x-9`.

Now, we can get the y-intercept by plugging in 0 for x so we get something like...`y=3(0)-9`. Or `y=0-9`. We now know the y-intercept is `-9`.

To find the x-intercept, we make y equal 0 so we get something like `0=3x-9`. Now our job is to find what x is by isolating it. So we first add both sides by 9...

`9=3x`, then we divide both sides by 3.

`x=3`.

Now we know the x and y-intercepts, we just plot them on the graph, and draw a straight line through both of the points and that's how we graph the whole line!

If you're still not sure about this, plug in any x-value and you should get the y-value that matches the graph. (provided that you drew straight enough)

Answer 2

x-intercept = 3 & y-intercept = -9.

Explanation:

`y=3x-9`
It is in the form `y=max+c` where c is the y-intercept.
`:.`y-intercept = -9.
When `y=0`,
`0=3x-9` or `x=3` or 3 is the x-intercept