1. Graph Linear Inequalities Teacher Notes
Here is our procedure for graphing linear inequalities.
Step 1 – Graph line
Step 2 – Draw the line
Step 3 – Test points not on the line
Step 4 – Shade the solution half-plane.

2. IQ.3 Graph Linear Inequalities
Graphs on the Half-Plane

3. 2-7 Solving Equations With Algebra Tiles powerpoint
Learning Target
M2.2.F Solve quadratic equations that have real roots by completing the square and by using the quadratic formula.

4. 2-7 Solving Equations With Algebra Tiles powerpoint
Learning Target
A-REIc I can represent and solve equations and inequalities graphically.
Graph linear inequalities or systems of inequalities by hand or with technology.
A-REI.12 Graph the solutions to a linear inequality in two variables as a half- plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

5. Launch
Graph the one-variable inequality.
5 – 3x > -7
5 – 3x ≤ -7

6. Types of Inequalities What are the types of inequalities? > < ≥≤
How do they look on coordinate grid?

7. Graph y ≤ 3x + 2
Step 1:
Graph y = 3x + 2
y-intercept
slope

8. Graph y ≤ 3x + 2 Step 1: Graph y = 3x + 2 Step 2: Draw line
y-intercept
Slope
Step 2: Draw line

9. So, (-2, -2) is not a solution to the inequality.
Graph y ≤ 3x + 2
Step 3: Test a point not on the line.
Let’s test (-2, -2)
(-2) ≤ 3(-2) + 2
-2 ≤
-2 ≤ -4
FALSE
So, (-2, -2) is not a solution to the inequality.

10. Graph y ≤ 3x + 2 Step 3: Test a point on the other side of line.
Let’s test (1, 1)
(1) ≤ 3(1) + 2
1 ≤ 3 + 2
1 ≤ 5
TRUE ×
So, (1, 1) is a solution to the inequality.
So, (1, -1) is a solution to the inequality.

11. Graph y ≤ 3x + 2 Step 4: Shade the solution half-plane.
The side of the line with (1, 1) is the solution to the inequality, so shade that side of the line.

12. ©Evergreen Public Schools 2010
Debrief
What is a dotted line used when graphing a linear inequality on a graph similar to when graphing a one-variable inequality on a number line?
How many points do you need to test to decide which side of a line to graph on an inequality? What are good points to test? Support your answer.
A dotted line is like an open circle when graphing a one-variable inequality on a number line.
You only need to test one point. If the point you pick results in a true inequality statement, then shade the side with that point. If not, then shade the other side of the line.
(0,0) is a good point to test as long as the line does not pass through the point.
©Evergreen Public Schools 2010

13. Ticket Out This is the graph of y < 3x + 2
Which of these points are a solution?
Show work to support whether or not the points are a solution.
Only (2, -3) is a solution.
(2, 8) is on the line, but since the line is dotted because the inequality is “<“, the point is not a solution.

14. Ticket Out This is the graph of y < 3x + 2
Which of these points are a solution?
Show work to support whether or not the points are a solution.
Only (2, -3) is a solution.
(2, 8) is on the line, but since the line is dotted because the inequality is “<“, the point is not a solution.

15. Ticket Out This is the graph of y < 3x + 2
Which of these points are a solution?
Show work to support whether or not the points are a solution.
Only (2, -3) is a solution.
(2, 8) is on the line, but since the line is dotted because the inequality is “<“, the point is not a solution.

16. Ticket Out This is the graph of y < 3x + 2
Which of these points are a solution?
Show work to support whether or not the points are a solution.
Only (2, -3) is a solution.
(2, 8) is on the line, but since the line is dotted because the inequality is “<“, the point is not a solution.