Graphing a Linear Inequality

• So far, we have been graphing linear equality lines (i.e. y = 2x + 1)

• Now let’s look at graphing linear inequality lines (i.e. y > 2x + 1)

•Graphing a linear inequality is very similar to graphing a linear equality.

Graphing a Linear Inequality

Step 1) Solve the inequality for y (or for x if there is no y).

Step 2) Change the inequality to an equation and graph like before

Step 3) If the inequality is < or > (not equals), the line

is dashed (- - - - - - ). If the inequality is ≤ or ≥, the line is solid (______).

Step 4) If the inequality is < or ≤, you shade below or to the left of the line.

If the inequality is > or ≥, you shade above or to the right of the line.

Step 1: Solve the inequality for y: y Step 1: Solve the inequality for y: y ≤≤ 2x+1 2x+1 Step 2: Graph the line y = 2x + Step 2: Graph the line y = 2x + 11Step 3: Because y ≤ Step 3: Because y ≤ 2x+1 and 2x+1 and not <,not <, the line the line will be will be solidsolid

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Step 4: Now shade the Step 4: Now shade the side of the line where side of the line where y < 2x+1 (y < 2x+1 (belowbelow the the line).line).

Graph: y- 2xGraph: y- 2x ≤≤ + 1 + 1

Graph -y – x < 2Graph -y – x < 2

Step 2: Graph the Step 2: Graph the equality y = -x – 2 equality y = -x – 2

Step 3: Because y > -x – Step 3: Because y > -x – 2 and 2 and notnot ≥, the line ≥, the line will be will be dotteddotted

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-1-2-3-4-5 0Step 4: Now shade the Step 4: Now shade the side of the line where side of the line where y > -x - 2 (y > -x - 2 (aboveabove the the line).line).

Step 1: Solve the inequality for y: y > -x Step 1: Solve the inequality for y: y > -x – 2– 2

Graph the inequality 3 – x > 0

Step 1: Solve the inequality for x 3 - x > 0 -x > -3 x < 3

Graph: x < 3

Step 2: Graph the line x = 3Step 3: Because x < 3, the line will be dottedStep 4: Now shade the side of the line where x < 3 (to the left of the line)

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Check if your graph is correct

• To check that the shading is correct, pick a point in the area and plug it into the inequality.

• If the inequality statement is true, the shading is correct. If the inequality statement is false, the shading is incorrect.

Check if your graph is correct

• Pick a point, (1,2), in the shaded area.• Substitute into the original inequality 3 – x > 0 3 – 1 > 0 2 > 0• True! The inequality has been graphed correctly.

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Given the inequality graphed below:a.) Write an inequality statement.b.) Name one ordered pair that is not in the solution set.c.) Name one ordered pair that is in the solution set.

Given the inequality graphed below:a.) Write an inequality statement.b.) Name one ordered pair that is not in the solution set.c.) Name one ordered pair that is in the solution set.

Write a system of inequalities for the dark blue solution shown on the graph below.

(Hint: you should write 2 different inequalities – one for each graph)

Write a system of inequalities for the green solution shown on the graph below.

(Hint: you should write 2 different inequalities – one for each graph)

Write a system of inequalities for the dark blue solution shown on the graph below.

(Hint: you should write 2 different inequalities – one for each graph)

Write a system of inequalities for the dark blue solution shown on the graph below.

(Hint: you should write 2 different inequalities – one for each graph)

Write a system of inequalities for the blue solution shown on the graph below.

(Hint: you should write 3 different inequalities – one for each graph)