Graph Linear Inequalities In Two Variables

Front

What is a linear inequality in two variables?

Back

An inequality that can be expressed in the form ax + by <, >, ≤, or ≥ c, where a, b, and c are constants.

Front

What does the solution set of a linear inequality represent?

Back

The set of all points (x, y) that satisfy the inequality.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid or dotted line. 2. Shade the appropriate region based on the inequality.

Front

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

Back

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

Front

What does the inequality symbol '>' mean?

Back

It means that the value on the left is greater than the value on the right.

Front

What does the inequality symbol '<' mean?

Back

It means that the value on the left is less than the value on the right.

Front

What does the inequality symbol '≥' mean?

Back

It means that the value on the left is greater than or equal to the value on the right.

Front

What does the inequality symbol '≤' mean?

Back

It means that the value on the left is less than or equal to the value on the right.

Front

How can you determine which side of the line to shade when graphing an inequality?

Back

Choose a test point not on the line (usually (0,0) if it's not on the line) and substitute it into the inequality. If the inequality holds true, shade the side containing the test point.

Front

What is the significance of the y-intercept in the graph of a linear inequality?

Back

It is the point where the line crosses the y-axis, which helps in graphing the inequality.