Graphing Linear Inequalities

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 (such as <, >, ≤, or ≥). It represents a region of the coordinate plane.

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the values of the variable can be greater than or equal to a certain value.

Front

What does the symbol '≤' mean in a linear inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the values of the variable can be less than or equal to a certain value.

Front

How do you graph a linear inequality?

Back

1. Start by graphing the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). 2. Shade the region that satisfies the inequality.

Front

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

Back

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

Front

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

Back

Choose a test point not on the line (commonly (0,0)). Substitute the coordinates into the inequality. If the inequality holds true, shade the side of the line containing the test point.

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 as a shaded region on the coordinate plane.

Front

What is the slope-intercept form of a linear equation?

Back

Front

How do you convert a linear equation to slope-intercept form?

Back

Front

What does it mean for a point to be a solution to a linear inequality?

Back

A point (x, y) is a solution to a linear inequality if it satisfies the inequality when the coordinates are substituted into the inequality.