Inequality Graphs

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

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…

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

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

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

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

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

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

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

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

Plenary

Plenary On the graph to the right, plot coordinates that satisfy the following inequality: x2 + 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?

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