Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

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

Back

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

Front

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

Back

The symbol '≤' means 'less than or equal to' and indicates that the value on the left is either less than or equal to the value on the right.

Front

How do you graph the inequality y > x + 1?

Back

To graph y > x + 1, first graph the line y = x + 1 as a dashed line (not including the line), then shade the area above the line.

Front

What is the solution set of an inequality?

Back

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

Front

Are points on the boundary line included in the solution set for 'y ≥ x + 1'?

Back

Yes, points on the boundary line are included in the solution set for 'y ≥ x + 1' because the inequality is 'greater than or equal to'.

Front

What does it mean if a point is not part of the solution set?

Back

If a point is not part of the solution set, it means that the coordinates of that point do not satisfy the inequality.

Front

How do you determine if a point (x, y) is a solution to an inequality?

Back

To determine if a point (x, y) is a solution, substitute the x and y values 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 (≥ or ≤), while a dashed line indicates they are not included (> or <).

Front

What is the graph of the inequality y < -2x - 3?

Back

To graph y < -2x - 3, graph the line y = -2x - 3 as a dashed line and shade the area below the line.