College Algebra - Section 2.5
By the end of the section, you should be able to:
- Graph two variable linear inequalities.
- Graph two variable absolute value inequalities.
Definitions:
- Linear Inequality: an inequality in two variables whose graph is a region of the coordinate plane bounded by a line
- Boundary: the line that separates the coordinate plane into two half-planes.
- Half-Plane: the section of the coordinate plane that includes the solutions to the linear inequality, or the section that does not include the solutions.
- Test Point: a point that is NOT on the boundary line that is used to see which half-plane shows the solutions of the linear inequality.
The shaded half-plane is the region where the solutions to the linear inequality exist.
Steps for Graphing Two Variable Inequalities
- Graph the Boundary Line
- Dotted line - - - for
- Solid line _____ for
- Choose a test point
- Plug point into function to see if the point is a solution.
- Shade the correct side of the boundary line
- If the test point was a solution, shade the side where the test point IS located.
- If the test point was NOT a solution, shade the side OPPOSITE of the test point.
Examples of Graphing Two Variable Inequalities
Examples of modeling/solving real world problems with two variable inequalites
Examples of Graphing Absolute Value Inequalities
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