Linear Inequalities

Front

What type of line is used when graphing a linear inequality with \( \leq \) or \( \geq \)?

Back

A solid line.

Front

What type of line is used when graphing a linear inequality with \( < \) or \( > \)?

Back

A dashed line.

Front

Which inequality represents a graph with a solid line and shading below?

Back

An example is \( y \leq 2x + 3 \).

Front

What does the inequality \( y > -\frac{4}{5}x - 1 \) indicate about the graph?

Back

The graph will have a dashed line and shading above the line.

Front

What is the correct graph for the inequality \( y < 2x + 3 \)?

Back

The graph will have a dashed line with shading below.

Front

Define a linear inequality.

Back

A linear inequality is an inequality that involves a linear function and can be expressed in the form \( ax + by < c \), \( ax + by \leq c \), \( ax + by > c \), or \( ax + by \geq c \).

Front

What does it mean if a linear inequality is graphed with a solid line?

Back

It means that the points on the line are included in the solution set (i.e., the inequality is \( \leq \) or \( \geq \)).

Front

What does it mean if a linear inequality is graphed with a dashed line?

Back

It means that the points on the line are not included in the solution set (i.e., the inequality is < or >).

Front

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

Back

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

Front

What is the solution set of a linear inequality?

Back

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