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 '>' mean in an inequality?

Back

The symbol '>' means 'greater than'. It indicates that the value on the left side of the symbol is larger than the value on the right side.

Front

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

Back

The symbol '<' means 'less than'. It indicates that the value on the left side of the symbol is smaller than the value on the right side.

Front

What type of line is used to represent the inequality y > x + 12?

Back

A dashed or dotted line is used to represent the inequality y > x + 12, indicating that points on the line are not included in the solution set.

Front

What does the solution set of an inequality represent?

Back

The solution set of an inequality represents all the points (x, y) that satisfy the inequality.

Front

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

Back

To determine if a point is a solution to an inequality, 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 set (for ≤ or ≥), while a dashed line indicates that points on the line are not included (for < or >).

Front

Is the point (0, -2) a solution to the inequality y > x + 12?

Back

No, the point (0, -2) is not a solution because substituting x = 0 gives -2 > 12, which is false.

Front

Is the point (3, 3) a solution to the inequality y < x + 12?

Back

Yes, the point (3, 3) is a solution because substituting x = 3 gives 3 < 15, which is true.

Front

What does it mean if a point lies above the line in a graph of an inequality?

Back

If a point lies above the line in a graph of an inequality, it means that the point satisfies the inequality.