Graphing Inequalities

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 for a point to be a solution to an inequality?

Back

A point is a solution to an inequality if it satisfies the inequality when substituted into it.

Front

What is the difference between an open dot and a closed dot when graphing inequalities?

Back

An open dot indicates that the point is not included in the solution set (used for < or >), while a closed dot indicates that the point is included (used for ≤ or ≥).

Front

How do you graph the inequality y > mx + b?

Back

To graph y > mx + b, first graph the line y = mx + b with an open dot, then shade the region above the line.

Front

What does the symbol '>' represent in an inequality?

Back

The symbol '>' means 'greater than'.

Front

What does the symbol '<' represent in an inequality?

Back

The symbol '<' means 'less than'.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution to a system of inequalities, substitute the point into each inequality and check if all inequalities are satisfied.

Front

What is the significance of the slope in the equation of a line?

Back

The slope indicates the steepness of the line and the direction of the relationship between the variables.

Front

What does the term 'system of inequalities' refer to?

Back

A system of inequalities is a set of two or more inequalities with the same variables.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality on the same coordinate plane and identify the region where all shaded areas overlap.