1. Graphs of Linear Inequalitiesx y
line with gradient m
and intercept c c
y = mx + c
y = mx + c
is the region below the line
y < mx + c
is the region above the line
y > mx + c
y < mx + c
y > mx + c

2. Decide which side is y < 2x
Example
y £ 2x
Draw the boundary line
y = 2x x y 1 2 5 3 4 –1 –2 –3 –4 –5
y = 2x x y
0 1 2 2 4
(1,1)
Decide which side is y < 2x
y £ 2x
Label the required region clearly.
Use a point to check.
Shade out the region not required.

3. Label the required region clearly. x
Example
x + y > 2
Draw the boundary line x y 1 2 5 3 4 –1 –2 –3 –4 –5
x + y = 2
x + y > 2
Label the required region clearly. x y 2 1 2
(0,0)
Decide which side is x + y > 2
Use a point to check.
Shade out the region not required.

4. Label the required region clearly. - 5
Example
2x - y £ 5
Draw the boundary line x y 1 2 5 3 4 –1 –2 –3 –4 –5
2x - y = 5
2x – y = 5 x y
2.5 1 3
2x - y £ 5
Label the required region clearly.
- 5
(0,0)
Decide which side is 2x - y £ 5
Use a point to check.
Shade out the region not required.