# Inequalities and graphs example 1

Graph the following inequality.

`x+2y>8`

Subtract `x` from both sides to get `y` on its own.

`x-x+2y>8-x`

`2y>8-x`

Divide both sides by 2 to get `y` on its own.

`(2y)/2>8/2-x/2`

`y>8/2-x/2`

`y>4-x/2`

`y>\-x/2+4`

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

`x=-2` | then | `y>\-(-2/2)+4=5` | ||

`x=-1` | then | `y>\-(-1/2)+4=4.5` | ||

`x=0` | then | `y>\-(0/2)+4=4` | ||

`x=1` | then | `y>\-(1/2)+4=3.5` | ||

`x=2` | then | `y>\-(2/2)+4=3` |

Now draw a graph and mark on the above points and don't forget to use just a dotted line.

Now pick a point NOT on the line:

Choose `x=0` and `y=3`

`y>4-x/2`

and `3>4-0/2`

`3>4`

This reads 3 is greater than 4 which is of course incorrect.

So this DOES **NOT** SATISFY THE INEQUALITY.

DON’T SHADE IT.

Do shade the other side.

** **

# Inequalities and graphs example 1

Graph the following inequality.

`x+2y>8`

Subtract `x` from both sides to get `y` on its own.

`x-x+2y>8-x`

`2y>8-x`

Divide both sides by 2 to get `y` on its own.

`(2y)/2>8/2-x/2`

`y>8/2-x/2`

`y>4-x/2`

`y>\-x/2+4`

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

`x=-2` | then | `y>\-(-2/2)+4=5` | ||

`x=-1` | then | `y>\-(-1/2)+4=4.5` | ||

`x=0` | then | `y>\-(0/2)+4=4` | ||

`x=1` | then | `y>\-(1/2)+4=3.5` | ||

`x=2` | then | `y>\-(2/2)+4=3` |

Now draw a graph and mark on the above points and don't forget to use just a dotted line.

Now pick a point NOT on the line:

Choose `x=0` and `y=3`

`y>4-x/2`

and `3>4-0/2`

`3>4`

This reads 3 is greater than 4 which is of course incorrect.

So this DOES **NOT** SATISFY THE INEQUALITY.

DON’T SHADE IT.

Do shade the other side.

** **