4.4 Inequalities of 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 (>, <, ≥, ≤) and involves two variables, typically x and y.

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions to the inequality, which is typically a region in the coordinate plane.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (for ≥ or ≤) or a dashed line (for > or <). 2. Shade the region that satisfies the inequality.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all ordered pairs (x, y) that satisfy the inequality.

Front

What does it mean for a point to be a solution to an inequality?

Back

A point is a solution to an inequality if, when the coordinates of the point are substituted into the inequality, the statement is true.

Front

How can you determine if a point is a solution to a given inequality?

Back

Substitute the x and y values of the point into the inequality. If the resulting statement is true, then the point is a solution.

Front

What is a boundary line in the context of inequalities?

Back

A boundary line is the line that represents the equation of the inequality. It divides the coordinate plane into regions that represent solutions and non-solutions.

Front

What is the significance of the slope in the context of linear inequalities?

Back

The slope of the line in a linear inequality indicates the steepness and direction of the line, affecting the region that is shaded in the graph.

Front

What are the four types of linear inequalities?

Back

The four types of linear inequalities are: 1. y > mx + b 2. y < mx + b 3. y ≥ mx + b 4. y ≤ mx + b.