Graphing Inequalities and Lines Summative 12.20.2024

Front

What does the inequality y < 2x + 3 represent when graphed?

Back

The area below the line y = 2x + 3, with a dashed line indicating that points on the line are not included in the solution set.

Front

What type of line is used when graphing the inequalities y ≤ 2x + 3 or y ≥ 2x + 3?

Back

A solid line is used, indicating that points on the line are included in the solution set.

Front

Which symbol indicates that the boundary line is not included in the solution set?

Back

The symbols < and > indicate that the boundary line is not included.

Front

What is the solution set of an inequality?

Back

The set of all points (x, y) that satisfy the inequality.

Front

How do you determine if a point is a solution to an inequality?

Back

Substitute the point's coordinates into the inequality and check if the statement is true.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

It means that the point is included in the solution set if the line is solid (≤ or ≥) and not included if the line is dashed (< or >).

Front

What is the significance of shading in a graph of an inequality?

Back

Shading indicates the region of the graph that contains all the solutions to the inequality.

Front

How can you tell which direction to shade when graphing an inequality?

Back

Test a point not on the boundary line (often (0,0)) to see if it satisfies the inequality; if it does, shade that side.

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables that are graphed together.

Front

How do you find the solution to a system of inequalities?

Back

The solution is the region where the shaded areas of all inequalities overlap.