Inequalities and Linear 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

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the ratio of the vertical change (rise) to the horizontal change (run).

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does it mean if a line has a slope of 0?

Back

A line with a slope of 0 is horizontal, meaning there is no vertical change as you move along the line.

Front

What does it mean if a line has an undefined slope?

Back

A line with an undefined slope is vertical, meaning it goes straight up and down with no horizontal change.

Front

Are points on a solid line included in the solution set of an inequality?

Back

Yes, points on a solid line are included in the solution set of an inequality.

Front

What does a dashed line represent in a graph of an inequality?

Back

A dashed line represents that the points on the line are not included in the solution set.

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 area above the line.