Graphing Inequalities

Front

What does the inequality y > -2x - 3 represent on a graph?

Back

The area above the line y = -2x - 3 is shaded, and the line is dashed, indicating that points on the line are not included in the solution.

Front

What does it mean when a graph is shaded above a line with a solid line?

Back

It indicates that the inequality is 'greater than or equal to' (≥), meaning points on the line are included in the solution.

Front

How do you identify the correct inequality from a graph?

Back

Look at the shading direction (above or below the line) and whether the line is solid or dashed to determine the inequality symbol.

Front

What is the significance of a dashed line in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set (used for 'greater than' or 'less than' inequalities).

Front

What does the inequality y ≤ 1 represent on a graph?

Back

The area below the line y = 1 is shaded, and the line is solid, indicating that points on the line are included in the solution.

Front

How do you determine if an inequality is true for a given point?

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is part of the solution set.

Front

What does the inequality y > -x - 5 indicate about the graph?

Back

The area above the line y = -x - 5 is shaded, and the line is dashed, indicating that points on the line are not included.

Front

What is the difference between y < 1/2x + 1 and y < 1/2x + 2?

Back

The first inequality represents a line that is higher than the second line, resulting in a different shaded area below each line.

Front

What does it mean when an inequality is written as y ≥ 2?

Back

It means that the area above the line y = 2 is shaded, and the line is solid, including points on the line.

Front

How can you tell if a graph represents y > 1/2x + 2?

Back

The area above the line y = 1/2x + 2 is shaded, and the line is dashed, indicating that points on the line are not included.