What is the term used to describe a mathematical statement that contains an inequality sign?
To graph an inequality, plot a line on a number line or coordinate plane. The line should include all points that would make the inequality true. For greater than or less than inequalities, use an open circle or open bracket to show the solution set.
Inequality: an expression that compares two values, where one is greater than or less than the other. Graph: a visual representation of a set of values. Solution: a value or set of values that makes an inequality true.
A graph of an inequality is a set of points on a coordinate plane that represents all the solutions of the inequality. The shaded region of a graph of an inequality is known as the 'feasible region' of the inequality. The union of two inequalities, such as x + y < 3 and x - y > 1, is a graphical representation of the intersection of two half-planes in a 3-dimensional space.
Did you know?
What are some of the similarities and differences between graphing linear inequalities and graphing linear equations?
What are some of the challenges you face when graphing inequalities?
How have your graphing skills improved since we started studying inequalities?
What strategies have you found to be most effective when graphing inequalities?
Brain break: Draw a banana with a cape and superhero mask flying over a bunch of broccoli buildings.
Question: You are a math teacher and you need to graph an inequality. How would you and your student explain the solution through a drawing? Clues: • Remember the inequality sign (>, <, ≥, ≤) and the equation's line of symmetry. • Mark the points where the inequality changes sign. • Consider the half-planes. In pairs: Select and solve one of the tasks: A. Draw the solution with a pencil and paper. B. Solve the inequality on a graphing calculator and explain the solution.
What does the shaded region of an inequality graph represent?
- The points that do not satisfy the inequality
- All possible solutions to the inequality
- The intersection of two or more inequalities
Which direction does the shading go for a greater than inequality?
- Up and to the right
- Down and to the left
- Up and to the left
How is a less than or equal to symbol represented on an inequality graph?
- A dashed line above y = mx + b
- A solid line above y = mx + b
- A solid line under y = mx + b
Which type of boundary line indicates that values on it are included in its solution set?
What does it mean if a point is in the shaded region of an inequality graph?
- It does not satisfy any of the inequalities being graphed.
- It satisfies at least one but not necessarily all inequalities being graphed.
- It satisfies all inequalities being graphed.
Work together in pairs: Describe how to graph a linear inequality in two variables.