Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

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 (since it's not inclusive). 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 values that make the inequality true.

Front

How can you determine if a point is part of the solution set for an inequality?

Back

To determine if a point is part of the solution set, substitute the coordinates of the point into the inequality. If the inequality holds true, the point is part of the solution set.

Front

What does it mean if a line is dashed in a graph of an inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set (for inequalities using < or >).

Front

What does it mean if a line is solid in a graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set (for inequalities using ≤ or ≥).

Front

How do you graph the inequality x ≤ -2?

Back

To graph x ≤ -2, draw a solid vertical line at x = -2 and shade to the left of the line.

Front

What is the difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' uses a dashed line and does not include the line in the solution set, while 'y ≤ mx + b' uses a solid line and includes the line.