# Inequalities and graphs example 2

Graph the following inequality:

`4y-x<=4`

Add `x` to both sides to get `y` on its own.

`4y-x<=4`

`4y-x+x<=4+x`

`4y<=4+x`

Divide both sides by 4 to get `y` on its own.

`(4y)/4<=4/4+x/4`

`y<=1+x/4`

`y<=x/4+1`

First, let's calculate some points on the graph.

`x=-2` | then | `y<=(-2/4)+1=(-1/2)+1=1/2` | ||

`x=-1` | then | `y<=(-1/4)+1=3/4` | ||

`x=0` | then | `y<=(0/4)+1=1` | ||

`x=1` | then | `y<=1/4+1=1\1/4` | ||

`x=2` | then | `y<=2/4+1=1\1/2` |

Now draw a graph and mark on the above points. Don’t forget to use a SOLID line.

Now pick a point **not** on the line.

Choose `x=0` and `y=0`

`y<=x/4+1`

`0<=0/4+1`

`0<=1`

This read 0 is less than or equal to 1. This is obviously correct.

This **DOES** satisfy the inequality.

SHADE IT.