# How do you graph the line x+2y=4?

Apr 8, 2017

$x + 2 y$ isn't a line but a 3D function.

#### Explanation:

As you have two different variables (x and y) you aren't looking at a linear function but at a 3d function instead. Make sure you have the correct heading (or perhaps its mistaken in your book?)!

However, this is what it'd look like:

If the heading was mistaken or you copied it down incorrectly, and you have a new linear graph you don't know how to plot, please let me know and I'll try to help you out :)

Apr 8, 2017

Identify the $x$ and $y$ intercepts, then draw the line through them.

#### Explanation:

Given:

$x + 2 y = 4$

Note that this equation is linear, since all of the terms in $x$ and $y$ are of degree at most $1$.

We can find the line's $x$ intercept by setting $y = 0$, or equivalently covering up the $y$ term to find:

$x = 4$

So the intersection with the $x$ axis (which has equation $y = 0$) is the point $\left(4 , 0\right)$.

Similarly, we can find the line's $y$ intercept by setting $x = 0$, or equivalently covering up the $x$ term to find:

$2 y = 4$

and hence:

$y = 2$

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

Now we can draw our line through those two points:

graph{(x+2y-4)((x-4)^2+y^2-0.02)(x^2+(y-2)^2-0.02) = 0 [-7.58, 12.42, -4.04, 5.96]}