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 (such as <, >, ≤, or ≥) and involves two variables, typically x and y.

Front

What does the graph of an inequality represent?

Back

The graph of an inequality represents all the solutions that satisfy the inequality, typically shaded on one side of a boundary line.

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

Back

Front

What is the slope-intercept form of a linear equation?

Back

Front

Back

Front

What does the term 'solution set' refer to in the context of inequalities?

Back

The solution set refers to all the ordered pairs (x, y) that satisfy the inequality.

Front

How can you test if a point is a solution to an inequality?

Back

To test if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the significance of the boundary line in graphing inequalities?

Back

The boundary line separates the graph into two regions, one representing solutions that satisfy the inequality and the other representing those that do not.

Front

What is the general form of a linear inequality?

Back