Solutions to 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 (>, <, ≥, ≤) instead of an equal sign.

Front

What does the solution set of a linear inequality represent?

Back

The solution set of a linear inequality represents all the points (x, y) that satisfy the inequality.

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 represents the solution set based on the inequality symbol.

Front

What does a dashed line indicate in the graph of a linear inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set (for < or > inequalities).

Front

What does a solid line indicate in the graph of a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set (for ≤ or ≥ inequalities).

Front

How can you determine if a point is a solution to a linear inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the significance of the shaded region in the graph of a linear inequality?

Back

The shaded region represents all the possible solutions to the inequality.

Front

What is the difference between a solution to a linear equation and a solution to a linear inequality?

Back

A solution to a linear equation is a specific point that makes the equation true, while a solution to a linear inequality includes a range of points that satisfy the inequality.

Front

If a point lies on a dotted line of a linear inequality, is it a solution?

Back

No, if a point lies on a dotted line, it is not included in the solution set.

Front

What does it mean if a point is above the line in a linear inequality graph?

Back

If a point is above the line in a linear inequality graph, it typically means that it satisfies the inequality (for y > mx + b type inequalities).