Day A: Graphing Inequalities in Two Variables #1

Front

What is an inequality in two variables?

Back

An inequality in two variables is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, or ≥) and involves two variables, typically x and y.

Front

What does the symbol '>' represent in an inequality?

Back

The symbol '>' means 'greater than'. For example, in the inequality y > -x + 2, y is greater than the expression -x + 2.

Front

What does the symbol '<' represent in an inequality?

Back

The symbol '<' means 'less than'. For example, in the inequality y < x - 6, y is less than the expression x - 6.

Front

What does the symbol '≥' represent in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. For example, in the inequality y ≥ 3, y is greater than or equal to 3.

Front

What does the symbol '≤' represent in an inequality?

Back

The symbol '≤' means 'less than or equal to'. For example, in the inequality y ≤ -x + 2, y is less than or equal to the expression -x + 2.

Front

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

Back

To graph y > -x + 2, first graph the line y = -x + 2 as a dashed line (since the inequality is not inclusive). Then shade the area above the line, indicating that y is greater than the line.

Front

How do you graph the inequality y ≤ 3?

Back

To graph y ≤ 3, draw a solid horizontal line at y = 3 (since the inequality is inclusive). Shade the area below the line, indicating that y is less than or equal to 3.

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 of the inequality. For example, in y < -x + 2, the line is dashed because points on the line are not part of the solution.

Front

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

Back

A solid line indicates that the points on the line are included in the solution set of the inequality. For example, in y ≥ -x + 2, the line is solid because points on the line are part of the solution.

Front

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

Back

To determine which side to shade, pick a test point not on the line (commonly (0,0)). Substitute the coordinates into the inequality. If the inequality holds true, shade the side containing the test point; otherwise, shade the opposite side.