1. Graphing inequalities in 2 variables
Lesson 39
Graphing inequalities in 2 variables

2. A linear inequality in 2 variables relates 2 variables, often x and y, with an inequality sign: <, >, <, > .
A solution (x,y) makes the inequality true when the values of x and y are substituted into the inequality.
Inequalities have an infinite number of solutions.

3. Determining if an ordered pair is a solution of a linear inequality
Is (2,9) a solution to y> -3x+5
9 > -3(2) +5
9 > -6+5
9 > -1
True, so this point is a solution

4. examples Is (0,0) a solution to y> 7+2x
Is (-3,1) a solution to 2x-3y > 7
Is (-3,4) a solution to -2y < 1-x

5. Finding solutions by graphing
Graph y = 4/3 x -2
Then graph each of the following points and tell if they are above the line, below the line, or on the line.
(6,2) (-3,-6) (1,4) (-5,-5) (0,-2) (4,-1)
Which points satisfy y < 4/3 x -2? Are these above or below the line?
Which points satisfy y > 4/3 x -2? Are these above or below the line?

6. The graph of a linear inequality in 2 variables is the set of all points that satisfy the inequality.
TO GRAPH AN INEQUALITY:
1) graph the related linear equation
2)make the line dashed when the < or > are used, and solid when < or > are used. This line is the boundary line. It separates the the plane into 2 half planes.
3) Shade the half-plane that includes the solutions of the inequality

7. Using a table of values to graph a linear inequality
Graph 3y+x> -9 by making a table of values or
Write inequality in slope intercept form
y > -1/3 x -3
Use solid line
Graph find an ordered pair that satisfies the inequality
Shade in the side

8. graph
5y + x < 20
-2y + 10x < -2
2x-3y > 7
3x +6y < 0

9. application
Nellie is making a peanut butter and jelly snack for a school function. Each tablespoon of jelly has 15 grams of carbs and each tablespoon of pb has 3 grams of carbs. She wants the snack to have no more than 90 grams of carbs. Graph the inequality that represents the possible amounts of each ingredient
15j + 3p < 90
Or p < -5j y< -5x +30