Front

What is a linear inequality in two variables?

Back

A linear inequality in two variables is an inequality that can be expressed 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 depicted as a shaded region on a graph.

Tags

CCSS.HSA.REI.D.12

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 appropriate region based on the inequality.

Tags

CCSS.HSA.REI.D.12

Front

What does a solid line indicate in the graph of a linear inequality?

Back

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

Tags

CCSS.HSA.REI.D.12

Front

What does a dotted line indicate in the graph of a linear inequality?

Back

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

Tags

CCSS.HSA.REI.D.12

Front

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

Back

You can test a point not on the line (like (0,0)) in the inequality. If the inequality holds true, shade the side containing that point.

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of the inequality symbol in determining the type of line used in graphing?

Back

The inequality symbol determines whether the line is solid or dotted: < or > results in a dotted line, while ≤ or ≥ results in a solid line.

Tags

CCSS.HSA.REI.D.12

Front

If the inequality is y < 2x + 3, what type of line will be used?

Back

A dotted line will be used, and the shading will be below the line.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

If a point lies on the line of a linear inequality, it is part of the solution set only if the line is solid (for ≤ or ≥). If the line is dotted, the point is not included.

Tags

CCSS.HSA.REI.D.12

Front

What is the first step in solving a linear inequality?

Back

The first step is to isolate the variable on one side of the inequality, similar to solving an equation.