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 (>, <, ≥, ≤).

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than'. It indicates that the value on the left is larger than the value on the right.

Front

What does the symbol '<' mean in an inequality?

Back

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

Front

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

Back

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

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left is either smaller 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 appropriate region based on the inequality.

Front

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

Back

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

Front

What does it mean to shade above the line in a graph of an inequality?

Back

Shading above the line indicates that the solutions to the inequality are all the points where the y-value is greater than the line (for inequalities like y > mx + b or y ≥ mx + b).

Front

What does it mean to shade below the line in a graph of an inequality?

Back

Shading below the line indicates that the solutions to the inequality are all the points where the y-value is less than the line (for inequalities like y < mx + b or y ≤ mx + b).

Front

How can you determine if a point is a solution to a linear inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.