Graphs of 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 such as <, >, ≤, or ≥.

Front

What does the symbol '≥' indicate when graphing?

Back

The symbol '≥' indicates that the line is solid and the area above the line is shaded.

Front

What does the symbol '<' indicate when graphing?

Back

The symbol '<' indicates that the line is broken (dashed) and the area below the line is shaded.

Front

How do you graph the inequality y < 2?

Back

Graph the line y = 2 as a broken line and shade the area below the line.

Front

What is the difference between a solid line and a broken line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≥ or ≤), while a broken line indicates that the points on the line are not included (> or <).

Front

When graphing y ≥ 3x + 1, what type of line is used?

Back

A solid line is used because the inequality includes '≥'.

Front

What does shading above the line indicate in a graph of an inequality?

Back

Shading above the line indicates that the solutions to the inequality are greater than the line's value.

Front

What does shading below the line indicate in a graph of an inequality?

Back

Shading below the line indicates that the solutions to the inequality are less than the line's value.

Front

How do you determine which side to shade when graphing y < mx + b?

Back

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

Front

What is the graph of the inequality y > -2?

Back

Graph the line y = -2 as a broken line and shade the area above the line.