Graphing Inequalities and Lines

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 '≤' represent?

Back

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

Front

What does the symbol '≥' represent?

Back

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

Front

How do you graph the inequality @@y eq 3x + 2@@?

Back

You would use a dashed line to represent the boundary line, indicating that points on the line are not included in the solution set.

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

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

Back

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

Front

Back

The solution set includes all points below the horizontal line at y = 2, not including the line itself.

Front

What does the graph of @@y eq mx + b@@ look like?

Back

It is a straight line with a slope of m and a y-intercept of b, but the line is dashed if the inequality is strict (not including the line).

Front

Back

Set x = 0. The y-intercept is the value of y when x is 0, which is 2.

Front

Back

The slope is -3/4, indicating that for every 4 units you move to the right, the line moves down 3 units.