Section 2 8 Graph Linear Inequalities in Two

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Section 2. 8: Graph Linear Inequalities in Two Variables

Section 2. 8: Graph Linear Inequalities in Two Variables

Linear inequality in two variables – can be written in one of these forms:

Linear inequality in two variables – can be written in one of these forms: Ax + By < C Ax + By > C

An ordered pair (x, y) is a solution of a linear inequality in two

An ordered pair (x, y) is a solution of a linear inequality in two variables if the inequality is true when the values of x and y are substituted into the inequality.

The graph of a linear inequality in two variables is the set of all

The graph of a linear inequality in two variables is the set of all points in a coordinate plane that represent solutions of the inequality. The boundary line divides the plane into two half-planes.

Graphing a Linear Inequality 1) Graph the boundary line for the inequality. Use a

Graphing a Linear Inequality 1) Graph the boundary line for the inequality. Use a dashed line for < or > and a solid line for < and >. 2) Test a point not on the boundary line to determine whether it is a solution of the inequality. If it is a solution, shade the halfplane containing the point. If it is not a solution, shade the other half-plane.

Graphing an absolute value inequality is similar to graphing a linear inequality, but the

Graphing an absolute value inequality is similar to graphing a linear inequality, but the boundary is an absolute value graph.

Example 1: Which ordered pair is a solution of 5 x – 2 y

Example 1: Which ordered pair is a solution of 5 x – 2 y < 6? a) b) c) d) (5, 5) (0, -3) (1, -2) (3, 3) (0, -3)

Example 2: Graph x < 5 on a coordinate plane.

Example 2: Graph x < 5 on a coordinate plane.

Example 3: Graph 3 x – 4 y > 12 on a coordinate plane.

Example 3: Graph 3 x – 4 y > 12 on a coordinate plane.

Example 4: You have two part-time summer jobs, one that pays $9 an hour

Example 4: You have two part-time summer jobs, one that pays $9 an hour and another that pays $12 an hour. You would like to earn at least $240 a week. Write an inequality describing the possible amounts of time you can schedule at both jobs. Graph the inequality. Identify three possible solutions of the inequality.

9 x + 12 y > 240 Sample answers: • 10 hours at $9

9 x + 12 y > 240 Sample answers: • 10 hours at $9 13 hours at $12 • 16 hours at $9 9 hours at $12 • 5 hours at $9 17 hours at $12

Example 5: Graph y < - |x + 2| - 1 on a coordinate

Example 5: Graph y < - |x + 2| - 1 on a coordinate plane. Down 1 unit Left 2 units Reflect over x-axis Shade graph

HOMEWORK pg. 135 – 136; 3 – 6, 8 – 24 even

HOMEWORK pg. 135 – 136; 3 – 6, 8 – 24 even