Graphing inequalities in 2 variables Lesson 39 Graphing inequalities in 2 variables

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.

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

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

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?

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

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

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

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 +30 y< -5x +30