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 '>' represent in inequalities?

Back

The symbol '>' means 'greater than'. For example, in the inequality y > -2x - 3, y is greater than the expression -2x - 3.

Front

What does the symbol '≥' represent in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value can be either greater than or exactly equal to the expression.

Front

How do you graph the inequality y > -2x - 3?

Back

To graph y > -2x - 3, first graph the line y = -2x - 3 with a dashed line (since it's not inclusive), then shade the area above the line.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set (≥ or ≤), while a dashed line indicates that the points on the line are not included (> or <).

Front

How do 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 x and y values 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 graph is shaded above a line?

Back

If a graph is shaded above a line, it indicates that the solutions to the inequality are all the points above that line, meaning the y-values are greater than the corresponding x-values.

Front

What does it mean if a graph is shaded below a line?

Back

If a graph is shaded below a line, it indicates that the solutions to the inequality are all the points below that line, meaning the y-values are less than the corresponding x-values.

Front

How do you write the inequality for a graph with a solid line and shaded above?

Back

The inequality for a graph with a solid line and shaded above is written as y ≥ mx + b, where m is the slope and b is the y-intercept.

Front

How do you write the inequality for a graph with a dashed line and shaded below?

Back

The inequality for a graph with a dashed line and shaded below is written as y < mx + b, where m is the slope and b is the y-intercept.