Graphing 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

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a boundary line. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

Front

What does the symbol '≤' mean in a linear inequality?

Back

It means 'less than or equal to', indicating that the values on the left can be equal to or less than the value on the right.

Front

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

Back

It means 'greater than or equal to', indicating that the values on the left can be equal to or greater than the value on the right.

Front

What is the significance of the boundary line in graphing inequalities?

Back

The boundary line divides the coordinate plane into two regions, one where the inequality holds true and one where it does not.

Front

How do you determine which side of the boundary line to shade?

Back

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

Front

What is the solution set of a linear inequality?

Back

The set of all points (x, y) that satisfy the inequality, represented graphically by the shaded region.

Front

What is a system of linear inequalities?

Back

A set of two or more linear inequalities that are considered simultaneously.

Front

How do you graph a system of linear inequalities?

Back

Graph each inequality on the same coordinate plane and identify the region where all shaded areas overlap.

Front

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

Back

If the point satisfies the inequality with '≤' or '≥', it is included in the solution set; if it satisfies '<' or '>', it is not included.