Graphing 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 (like <, >, ≤, 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, x > 3 means x is any number greater than 3.

Front

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

Back

The symbol '<' means 'less than'. For example, y < 5 means y is any number less than 5.

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

How do you graph the inequality y > -2?

Back

To graph y > -2, draw a dashed horizontal line at y = -2 and shade the region above the line.

Front

What type of line is used for inequalities with '≥' or '≤'?

Back

A solid line is used for inequalities with '≥' or '≤' to indicate that points on the line are included in the solution set.

Front

What does the point (-1, 0) represent in the context of the inequality y > -2?

Back

The point (-1, 0) does not satisfy the inequality y > -2 because 0 is not greater than -2.

Front

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

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality and check if the statement is true.

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 (for '≥' or '≤'), while a dashed line indicates that points on the line are not included (for '>' or '<').

Front

What does the inequality y < x + 12 represent graphically?

Back

The inequality y < x + 12 represents the region below the line y = x + 12, which has a slope of 1 and a y-intercept of 12.