Linear Inequalities: Shading & Lines

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality signs such as <, >, ≤, or ≥.

Front

What does the inequality sign '≤' mean?

Back

The sign '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

What does the inequality sign '≥' mean?

Back

The sign '≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

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 region that satisfies the inequality.

Front

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

Back

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

Front

What does it mean to shade above a line in a graph?

Back

Shading above a line indicates that the solutions to the inequality are all the points above the line, meaning the y-values are greater than the line's value.

Front

What does it mean to shade below a line in a graph?

Back

Shading below a line indicates that the solutions to the inequality are all the points below the line, meaning the y-values are less than the line's value.

Front

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

Back

To determine which side to shade, pick a test point not on the line (usually (0,0) if it's not on the line) and substitute it into the inequality. If the inequality holds true, shade that side.

Front

What is a test point in graphing inequalities?

Back

A test point is a point used to determine which side of the line to shade when graphing an inequality. It is typically chosen to be easy to calculate, like (0,0).

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality, represented graphically by the shaded region.