Graphing Linear Inequalites

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (e.g., <, >, ≤, ≥).

Front

What does the symbol '≤' represent?

Back

The symbol '≤' means 'less than or equal to.' It indicates that one value is either less than or equal to another value.

Front

What does the symbol '>' represent?

Back

The symbol '>' means 'greater than.' It indicates that one value is larger than another value.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the appropriate region based on the inequality.

Front

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

Back

A dashed line indicates that the points on the line are not included in the solution (for < or >), while a solid line indicates that the points on the line are included (for ≤ or ≥).

Front

What does the inequality 'y < 2x + 3' represent graphically?

Back

It represents the region below the line y = 2x + 3, not including the line itself.

Front

What is the solution set of the inequality 'x ≥ 4'?

Back

The solution set includes all values of x that are greater than or equal to 4.

Front

How do you determine which side of the line to shade when graphing an inequality?

Back

Choose a test point not on the line (commonly (0,0)), substitute it into the inequality, and if the inequality holds true, shade the side containing the test point.

Front

What is the graphical representation of 'y ≥ -x + 1'?

Back

It includes the area above and on the line y = -x + 1, including the line itself.

Front

What does the inequality 'x < 3' represent?

Back

It represents all values of x that are less than 3, graphed as a dashed vertical line at x = 3, shading to the left.