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 '>' mean in an inequality?

Back

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

Front

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

Back

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

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). 2. Shade the region that satisfies the inequality.

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 do you determine if a point is in the solution set of an inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is in the solution set.

Front

What is the inequality that represents a limo driver needing to make more than $450 if he charges $375 and $0.85 per mile?

Back

0.85x + 375 > 450

Front

What does it mean if a point lies on the boundary line of a graph of an inequality?

Back

If a point lies on the boundary line of a graph of an inequality, it is included in the solution set if the line is solid (≤ or ≥) and not included if the line is dashed (< or >).

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

If the inequality is y < 2x + 3, what is the slope of the boundary line?

Back

The slope of the boundary line is 2.