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 (e.g., <, >, ≤, ≥).

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shaded on one side of a boundary line.

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 that points on the line are not included (>, <).

Front

How do you determine which side of the line to shade in a linear inequality?

Back

To determine which side to shade, test a point not on the line (usually (0,0)). If the point satisfies the inequality, shade the side containing that point.

Front

What does the inequality y > 3x - 2 mean in terms of graphing?

Back

It means that the region above the line y = 3x - 2 is part of the solution set, and the line itself is not included.

Front

What does the inequality y ≤ -3/4x + 3 indicate about the boundary line?

Back

It indicates that the boundary line is solid (included in the solution) and the region below the line is shaded.

Front

What is the significance of the slope in a linear inequality?

Back

The slope indicates the steepness of the line and the direction of the inequality (positive slope means the line rises, negative slope means it falls).

Front

How can you tell if a graph is shaded above or below the line?

Back

If the inequality symbol is '>' or '≥', the graph is shaded above the line; if it is '<' or '≤', it is shaded below.

Front

What does the term 'solution set' refer to in the context of linear inequalities?

Back

The solution set refers to all the points (x, y) that satisfy the inequality.

Front

What is the first step in graphing a linear inequality?

Back

The first step is to graph the corresponding linear equation as if it were an equality.