1. 6.5 Graphing Linear Inequalities in Two Variables
Wow, graphing really is fun!

2. Learning Goal #1 for Focus 4 (HS.A-CED.A.2, HS.REI.ID.10 & 12, HS.F-IF.B.6, HS.F-IF.C.7, HS.F-LE.A.2): The student will understand that linear relationships can be described using multiple representations. 4 3 2 1
In addition to level 3.0 and above and beyond what was taught in class,  the student may:
· Make connection with other concepts in math
· Make connection with other content areas.
The student will understand that linear relationships can be described using multiple representations.
- Represent and solve equations and inequalities graphically.
- Write equations in slope-intercept form, point-slope form, and standard form.
- Graph linear equations and inequalities in two variables.
- Find x- and y-intercepts.
The student will be able to:
- Calculate slope.
- Determine if a point is a solution to an equation.
- Graph an equation using a table and slope-intercept form.
With help from the
teacher, the student has
partial success with calculating slope, writing an equation in slope-intercept form, and graphing an equation.
Even with help, the student has no success understanding the concept of a linear relationships.

3. What is a linear inequality?
A linear inequality in x and y is an inequality that can be written in one of the following forms.
ax + by < c
ax + by ≤ c
ax + by > c
ax + by ≥ c

4. An ordered pair (a, b) is a solution of a linear equation in x and y if the inequality is TRUE when a and b are substituted for x and y, respectively.
For example: is (1, 3) a solution of x – y < 2?
4(1) – 3 < 2
1 < 2 This is a true statement so (1, 3) is a solution.

5. Check whether the ordered pairs are solutions of 2x - 3y ≥ -2. a
Check whether the ordered pairs are solutions of 2x - 3y ≥ -2. a. (0, 0) b. (0, 1) c. (2, -1)
(x, y)
Substitute
Conclusion A
(0,0)
2(0) – 3(0) =
0 ≥ -2
(0,0) is a solution. B
(0,1)
2(0) – 3(1)
-3 ≥-2
(0, 1) is NOT a solution. C
(2,-1)
2(2) – 3(-1)
7 ≥ -2
(2, -1) is a solution.

6. Graph the inequality 2x – 3y ≥ -2
Every point in the shaded region is a solution of the inequality and every other point is not a solution. 3 2 1 -1 -2 -3

7. Steps to graphing a linear inequality:
Sketch the graph of the corresponding linear equation.
Use a dashed line for inequalities with < or >.
Use a solid line for inequalities with ≤ or ≥.
This separates the coordinate plane into two half planes.

8. Test a point in one of the half planes to find whether it is a solution of the inequality.
If the test point is a solution, shade its half plane. If not shade the other half plane.

9. Sketch the graph of 6x + 5y ≥ 30
Use x- and y-intercepts: (0, 6) & (5, 0) This will be a solid line.
Test a point. (0,0) 6(0) + 5(0) ≥ 30 0 ≥ 30 Not a solution.
Shade the side that doesn’t include (0,0). 6 4 2 -2 -4 -6

10. Sketch the graph y < 6. This will be a dashed line at y = 6.
Test a point. (0,0) 0 < 6 This is a solution.
Shade the side that includes (0,0). 6 4 2 -2 -4 -6

11. Sketch the graph of 2x – y ≥ 1
Use x- and y-intercepts: (0, -1) & (1/2, 0)
This will be a solid line.
Test a point. (0,0) 2(0) - 0 ≥ 1 0 ≥ 1 Not a solution.
Shade the side that doesn’t include (0,0). 3 2 1 -1 -2 -3