Graphing Inequalities 2.6

Front

What is an inequality in mathematics?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality involves representing the set of solutions on a number line or coordinate plane, indicating which values satisfy the inequality.

Front

What is the difference between a solid line and a dashed line when graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set (for 'greater than or equal to' or 'less than or equal to'), while a dashed line indicates that the points on the line are not included (for 'greater than' or 'less than').

Front

How do you determine the solution set for a linear inequality?

Back

To determine the solution set, you first graph the boundary line of the inequality, then shade the region that satisfies the inequality based on the direction of the inequality sign.

Front

What is the significance of the test point in graphing inequalities?

Back

A test point is a point not on the boundary line used to determine which side of the line to shade. If the test point satisfies the inequality, that side is shaded.

Front

What does the solution set of an inequality represent?

Back

The solution set of an inequality represents all the possible values that satisfy the inequality.

Front

How can you identify if a point is part of the solution set for an inequality?

Back

To identify if a point is part of the solution set, substitute the coordinates of the point into the inequality. If the inequality holds true, the point is part of the solution set.

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is typically written as Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

Front

What are the steps to graph a linear inequality in two variables?

Back

1. Rewrite the inequality in slope-intercept form (if necessary). 2. Graph the boundary line. 3. Determine if the line is solid or dashed. 4. Choose a test point to determine which side to shade.

Front

What is the role of the boundary line in graphing inequalities?

Back

The boundary line separates the coordinate plane into two regions, one of which contains the solutions to the inequality.