1. Inequality Graphs

2. Starter 1) Solve the following Inequalities: 3x + 5 > 26
b) 5x + 4 < 3x + 10
c) 8 – x ≥ 16
2) Draw the graph of y = 2x + 3

3. Inequality Graphs
Just like an equation, an inequality can be plotted as a graph
The difference will be that there is a range of possible values
You will be looking at shading regions that satisfy a particular condition…

4. SOLID line if less/greater than or equal to
Inequality Graphs
SOLID line if less/greater than or equal to
(≤ or ≥)
On a set of axes, show the set of values that satisfy the inequality;
x ≤ 2
Draw the line showing;
x = 2
But the inequality is saying a range of values…
x = 2

5. DOTTED line if less/greater than but not equal to
Inequality Graphs
DOTTED line if less/greater than but not equal to
(< or >)
On a set of axes, show the set of values that satisfy the inequality;
y < -5
Draw the line showing;
y = -5
But the inequality is saying a range of values…
y = -5

6. Inequality Graphs
On a set of axes, show the set of values that satisfy the inequality;
y > x
Draw the line showing;
y = x
But the inequality is saying a range of values…
y = x

7. Inequality Graphs
On a set of axes, show the set of values that satisfy the inequalities;
y < -1
x ≤ -6
Draw the lines showing;
y = -1
x = -6
But the inequality is saying a range of values…
y = -1
x = -6

8. Inequality Graphs
On a set of axes, show the set of values that satisfy the inequality;
y ≤ x + 3
Draw the line showing;
y = x + 3
But the inequality is saying a range of values…
y = x + 3 x 1 2 y 3 4 5

9. Inequality Graphs
On a set of axes, show the set of values that satisfy the inequality;
y > 5 - x
Draw the line showing;
y = 5 - x
But the inequality is saying a range of values…
y = 5 - x x 1 2 y 5 4 3

10. Inequality Graphs x 1 2 x 1 2 y 2 4 y 1 -1
On a set of axes, show the set of values that satisfy the inequalities;
y < 2x
y ≥ 1 - x
Draw the line showing;
But the inequality is saying a range of values…
y = 2x
y = 1 - x
y = 2x
y = 1 - x x 1 2 x 1 2 y 2 4 y 1 -1

11. Inequality Graphs x 1 2 x 1 2 y -5 -3 -1 y -2 -1
On a set of axes, show the set of values that satisfy the inequalities;
y < 2x - 5
y ≥ x - 2
Draw the line showing;
But the inequality is saying a range of values…
y = 2x - 5
y = x - 2 x 1 2 x 1 2 y -5 -3 -1 y -2 -1
y = x - 2
y = 2x - 5

12. Plenary

13. Plenary
On the graph to the right, plot coordinates that satisfy the following inequality:
x y2 ≤ 25
(choose integer values and put a cross on each coordinate that works!)
 What do you think the ‘boundary line’ for this would look like?

14. Summary We have recapped our knowledge of plotting graphs
We have seen that Inequalities can also be plotted as graphs
We also now know how to show regions that satisfy 2 Inequalities