Section 2 8 Graph Linear Inequalities in Two
- Slides: 13
Section 2. 8: Graph Linear Inequalities in Two Variables
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 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 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 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 boundary is an absolute value graph.
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 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 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 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 plane. Down 1 unit Left 2 units Reflect over x-axis Shade graph
HOMEWORK pg. 135 – 136; 3 – 6, 8 – 24 even
- Inequality graph
- Write a system of linear inequalities
- Linear inequalities in two variables
- Two step linear inequalities
- 2-5 linear inequalities in two variables
- Linear inequalities in two variables calculator
- Steps in graphing linear inequalities in two variables
- 2-5 linear inequalities in two variables
- Graphing linear inequalities on a number line
- Parabola inequalities
- Shading quadratic inequalities
- Solving compound inequalities worksheet
- Quadratic shader
- Bounded or unbounded graph