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 ≥.

Front

What does the symbol '≥' indicate in an inequality?

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

What does the symbol '≤' indicate in an inequality?

Back

The symbol '≤' indicates that the value on the left is less than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a boundary line. 2. Use a solid line for '≥' or '≤' and a dashed line for '>' or '<'. 3. Shade the region that satisfies the inequality.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all points (x, y) that make the inequality true.

Front

How can you tell if a point is in the solution set of an inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is in the solution set.

Front

What is the significance of a solid boundary line in graphing inequalities?

Back

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

Front

What is the significance of a dashed boundary line in graphing inequalities?

Back

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

Front

What does the inequality 'y < 4x - 2' represent graphically?

Back

It represents the region below the line y = 4x - 2, not including the line itself.

Front

How do you determine the boundary line of an inequality from its equation?

Back

To determine the boundary line, rewrite the inequality as an equation (e.g., y = mx + b) and graph it.