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 symbol '≥' indicate in a linear inequality?

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

What does the symbol '<' indicate in a linear inequality?

Back

The symbol '<' indicates that the value on the left is less than the value on the right.

Front

How do you determine if a line is solid or dashed when graphing an inequality?

Back

A solid line is used if the inequality includes 'or equal to' (≥ or ≤). A dashed line is used if the inequality is strictly greater than or less than (> or <).

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality.

Front

How do you graph the inequality y ≥ -2x + 1?

Back

Graph the line y = -2x + 1 as a solid line and shade the region above the line.

Front

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

Back

Shading above the line represents all the points where the y-value is greater than the value of the linear expression.

Front

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

Back

Shading below the line represents all the points where the y-value is less than the value of the linear expression.

Front

Which of the following points is NOT part of the solution set for the inequality y < -2x + 1? (0, 0), (-10, -10), (-1, 5), (5, 20)

Back

The point (-10, -10) is NOT part of the solution set.

Front

What is the importance of the equal sign in an inequality?

Back

The equal sign indicates that the boundary line is included in the solution set, resulting in a solid line.