Graphing Linear Inequalites

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

What does the symbol '≤' represent?

Back

The symbol '≤' means 'less than or equal to.' It indicates that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol '≥' represent?

Back

The symbol '≥' means 'greater than or equal to.' It indicates that the value on the left can be greater than or equal to the value on the right.

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 region that satisfies the inequality.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x=0.

Front

How do you find the y-intercept from the equation y = mx + b?

Back

In the equation y = mx + b, the y-intercept is the value of b.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What does it mean if a line is dashed in a graph of an inequality?

Back

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

Front

What does it mean if a line is solid in a graph of an inequality?

Back

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

Front

How do you determine which side of the line to shade in a graph of an inequality?

Back

To determine which side to shade, pick a test point (usually (0,0)) and substitute it into the inequality. If the inequality holds true, shade the side containing the test point.