# How do you graph x+3y=6 using intercepts?

##### 1 Answer
Jan 21, 2017

Find the intercepts by setting $x = 0$ or $y = 0$ and solving, then draw a line through them...

#### Explanation:

Given:

$x + 3 y = 6$

we can find the intercepts by setting $x = 0$ or $y = 0$ and solving. This is equivalent to crossing out the term involving $x$ or that involving $y$.

In any case, putting $x = 0$ we have:

$3 y = 6$

and hence $y = \frac{6}{3} = 2$

So the intersection with the $y$ axis (which has equation $x = 0$) is at the point $\left(0 , 2\right)$

Putting $y = 0$ we have:

$x = 6$

So the intersection with the $x$ axis is at $\left(6 , 0\right)$

Since there are no terms of degree $> 1$, the given equation describes a line through these two intercepts:

graph{(x+3y-6)(x^2+(y-2)^2-0.02)((x-6)^2+y^2-0.02) = 0 [-7.71, 12.29, -3.8, 6.2]}