Graphing Linear Inequalities Review

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

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed line (for < or >) or a solid line (for ≤ or ≥). Then shade the appropriate region based on the inequality.

Front

What does a dashed line indicate in graphing linear inequalities?

Back

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

Front

What does a solid line indicate in graphing linear inequalities?

Back

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

Front

In the inequality y < 3x - 3, which direction do you shade?

Back

Shade below the line because the inequality is less than (<).

Front

In the inequality x ≥ 2, which side of the line do you shade?

Back

Shade to the right of the line because the inequality is greater than or equal to (≥).

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all ordered pairs (x, y) that satisfy the inequality.

Front

How do you determine if an ordered pair is a solution to an inequality?

Back

Substitute the x and y values of the ordered pair into the inequality. If the inequality holds true, then it is a solution.

Front

What does the inequality y ≥ -5/4 x + 3 represent graphically?

Back

It represents a solid line with shading above the line, indicating that points on the line and above are included in the solution set.

Front

What is the significance of the slope in a linear inequality?

Back

The slope indicates the steepness of the line and the direction of the inequality (positive slope means the line rises, negative slope means it falls).