Do Now

1) Make 4 graphs on each side of your graph paper (8 graphs total).

2) Use the first graph to find the solution to the system:

x – y = 5

3x + y = 3

6

4

2

-2

-4

-6

-10 -5 5 10

Extra Credit Answer

Roger – Dressing on Pink Plate

Ted – Potatoes on Black Plate

Tom – Salad on Green Plate

Pam – Turkey on Purple Plate

Donna – Peas on White Plate

Graphing Linear Inequalities with

2 Variables

Checking Solutions• An ordered pair (x,y) is a solution if it

makes the inequality true.

• Are the following solutions to:

• 3x + 2y ≥ 2• (0,0) (2,-1) (0,2)3(0) + 2(0) ≥ 2 0 ≥ 2Not a solution

3(2) + 2(-1) ≥ 2 4 ≥ 2 Is a solution

3(0) + 2(2) ≥ 2 4 ≥ 2 Is a solution

Steps to Graphing Linear Inequalities 1.Change the inequality into slope-intercept form, y = mx + b. Graph points, but don’t draw line.

* (don’t forget to reverse if you divide both sides by a negative)

2.If > or < , the line should be dashed. If > or < , the line should be solid.

** (open circle = dashed line, closed circle = solid line)

3.If > or > , shade above the line. If < or < , shade below the line.

The graph of an inequality is the graph of all the solutions of the inequality

• 3x+ 2y ≥ 2• y ≥ -3/2x + 1 (put into slope intercept to

graph easier)• Graph points using slope and y-intercept• Before you connect the points check to see if the

line should be solid or dashed• solid if ≥ or ≤ and dashed if < or >• Shade: above if ≥ or > and below if ≤ or <

y ≥ -3/2x + 11) Graph points on the line. (the line is solid ≥)

2) Shade. (shade above for ≥)

* If you are asked for a point in the solution set, pick any shaded point.

Example:y

2

3x 4

6

4

2

5

2x 3y12

Example:

6

4

2

5

2. 3 6x y y 1

3x 2

Graph: y < 6

Example:3. x 1

6

4

2

-2

-5 5