Graphing Linear Inequalities

Front

What is a linear inequality?

Back

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

Front

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

Back

The symbol '<' indicates that the value on the left is less than the value on the right.

Front

How do you determine if a boundary line is solid or dashed in a graph of a linear inequality?

Back

A solid boundary line is used if the inequality includes 'or equal to' (≥ or ≤). A dashed boundary line is used if the inequality does not include 'or equal to' (> or <).

Front

What is the general form of a linear inequality in two variables?

Back

The general form of a linear inequality in two variables is Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

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. A positive slope means the line rises from left to right, while a negative slope means it falls.

Front

How can you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, use a test point to determine which side of the line to shade, indicating the solution set.

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

If a point lies on the boundary line, it satisfies the equation of the line. Whether it is included in the solution set depends on whether the inequality is strict or includes equality.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary line, while a non-strict inequality (≤ or ≥) includes the boundary line.

Front

How do you write an inequality from a graph?

Back

To write an inequality from a graph, identify the slope and y-intercept of the boundary line, determine if the line is solid or dashed, and decide the direction of the inequality based on the shaded region.