# Inequalities and graphs example 4

Shade the region on the graph that would satisfy all the following inequalities, label this region R.

x<3       y>\-2       y<\x

Take each inequality separately

x<3

First let’s calculate points on the graph

y=-2       then      x is <3

y=-1       then      x is still <3

y=0             then      x is still <3

y=1             then      x is still <3

y=2             then      x is still <3

Now draw a graph and mark the above points.

Don’t forget to use a dotted line.

Now pick a point NOT on the line.

Choose x=0   y=0

x<3

0<3

This reads zero is less than three.

This DOES satisfy the inequality, SHADE IT.

Take the next inequality

y>\-2

First let’s calculate points on the graph

x=-2       then      y is >\-2

x=-1       then      y is >\-2

x=0             then      y is >\-2

x=1             then      y is >\-2

x=2             then      y is >\-2

Now draw a graph and mark the above points. Don’t forget to use a DOTTED LINE.

Now pick a point NOT on the line.

Choose x=0     y=0

y>\-2

0>\-2

This reads zero is greater than minus two.

This DOES satisfy the inequality, SHADE IT.

Take the final inequality

y<x

First let’s calculate points on the graph

x=-2       then      y <-2

x=-1       then      y <-1

x=0             then      y <0

x=1             then      y <1

x=2             then      y <2

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

Now pick a point NOT on the line.

Choose x=0       y=0

y<\x

1<\0

This reads one is less than zero, which is obviously wrong and therefore this does NOT satisfy the inequality, SHADE THE OTHER HALF.

Now plot all three graphs.

R satisfies all the inequalities.