Graph Linear Inequalities In Two Variables

Front

What is a linear inequality in two variables?

Back

A linear inequality in two variables is an inequality that can be written in the form ax + by < c, ax + by > c, ax + by ≤ c, or ax + by ≥ c, where a, b, and c are constants.

Front

What does the solution set of a linear inequality represent?

Back

The solution set of a linear inequality represents all the points (x, y) that satisfy the inequality, often visualized as a shaded region on a graph.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dotted line (for < or >). 2. Shade the region that satisfies the inequality.

Front

What does a dotted line indicate when graphing a linear inequality?

Back

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

Front

What does a solid line indicate when graphing a linear inequality?

Back

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

Front

Is the point (0,0) a solution to the inequality y > -x + 1?

Back

No, (0,0) does not satisfy the inequality y > -x + 1.

Front

Is the point (1, 2) a solution for the inequality y ≤ -x + 3?

Back

Yes, (1, 2) satisfies the inequality y ≤ -x + 3.

Front

How can you tell if an inequality will have a dotted line?

Back

If the inequality symbol is greater than (>) or less than (<), the line will be dotted.

Front

Which point is NOT part of the solution set for the inequality y < 2x + 1?

Back

(3,0) is NOT part of the solution set.

Front

Which point is part of the solution set for the inequality y > -x + 1?

Back

(1,3) is part of the solution set.