Question

How do you graph `y – 2x< 4`?

Answer 1

graph{y<2x+4 [-10, 10, -5, 5]}

Explanation:

First we'll move the `2x` to the right hand side (RHS for short)

`y-2x<4`
`y<2x+4`

Next, lets ignore the fact that there is an inequality, lets just see what happens if the `<` were an `=`:

`y=2x+4`

So lets graph this line. It looks something like this:

graph{y=2x+4 [-10, 10, -5, 5]}

But then we go back to the original equation and care about the `<` sign. What this sign means graphically is that the area on one side of the line will be coloured in. How do we know which one? The simplest way would be to sub in some coordinates and see it if works or not.

Subbing in `(0,0)`:
`0<2(0)+4`
`0<4`

Because we know 4 is definitely bigger than 0, it means that (0,0) must lie in the coloured area! We now know to shade the area right of the line. But the question says `<`, so anything on the line `y=2x+4` isnt actually included. To show this we dash the line in the graph, and it finally looks like this:

graph{y<2x+4 [-10, 10, -5, 5]}

And we're done.