Question

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

Answer 1

`x + 2y` 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 :)

Answer 2

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

Explanation:

Given:

`x+2y = 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 `(4, 0)`.

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

`2y=4`

and hence:

`y = 2`

So the intersection with the `y` axis (which has equation `x=0`) is the point `(0, 2)`.

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]}