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 a value can be either less than or exactly equal to another value.

Front

What does the symbol '≥' represent?

Back

The symbol '≥' means 'greater than or equal to.' It indicates that a value can be either greater than or exactly equal to another value.

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 is the difference between a dashed line and a solid line in graphing inequalities?

Back

A dashed line indicates that points on the line are not included in the solution (for < or >), while a solid line indicates that points on the line are included (for ≤ or ≥).

Front

What does it mean to shade above a line in a graph?

Back

Shading above a line indicates that the solutions to the inequality are all the points where the y-value is greater than the y-value of the line.

Front

What does it mean to shade below a line in a graph?

Back

Shading below a line indicates that the solutions to the inequality are all the points where the y-value is less than the y-value of the line.

Front

If the inequality is y < 2x + 3, how would you graph it?

Back

Graph the line y = 2x + 3 as a dashed line and shade below it to represent all points where y is less than 2x + 3.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality, often represented graphically on a number line or coordinate plane.

Front

How do you determine which side to shade when graphing an inequality?

Back

To determine which side to shade, pick a test point not on the line (commonly (0,0)) and substitute it into the inequality. If the inequality holds true, shade the side containing the test point.