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

Oct 9, 2017

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 $3 x$ from both sides so we get something like $- y = - 3 x + 9$.

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

Now, we can get the y-intercept by plugging in 0 for x so we get something like...$y = 3 \left(0\right) - 9$. 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 $0 = 3 x - 9$. Now our job is to find what x is by isolating it. So we first add both sides by 9...

$9 = 3 x$, 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)

Oct 9, 2017

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