13-8 Inequalities in Two Variables

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 solution of an inequality represent?

Back

The solution of an inequality represents all the ordered pairs (x, y) that satisfy the inequality, forming a region on the coordinate plane.

Front

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

Back

To determine if an ordered pair (x, y) is a solution to an inequality, substitute the x and y values into the inequality and check if the statement is true.

Front

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

Back

The symbol '>' indicates that the value on the left is greater than the value on the right.

Front

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

Back

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

Front

What type of line is used to represent the inequality y < mx + b?

Back

A dashed line is used to represent the inequality y < mx + b, indicating that points on the line are not included in the solution.

Front

What type of shading is used for the inequality y < mx + b?

Back

Shading is done below the dashed line for the inequality y < mx + b, indicating that all points below the line are solutions.

Front

What type of line is used to represent the inequality y ≥ mx + b?

Back

A solid line is used to represent the inequality y ≥ mx + b, indicating that points on the line are included in the solution.

Front

What type of shading is used for the inequality y ≥ mx + b?

Back

Shading is done above the solid line for the inequality y ≥ mx + b, indicating that all points above the line are solutions.

Front

What is the graphical representation of the inequality y < -\frac{1}{3}x - 2?

Back

The graphical representation includes a dashed line for y = -\frac{1}{3}x - 2 and shading below the line.