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 '>' represent in an inequality?

Back

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

Front

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

Back

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

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

Front

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

Back

1. Graph the line y = 2x + 3 with a dashed line. 2. Shade the area above the line to represent all points where y is greater than 2x + 3.

Front

What does shading above a line in a graph indicate?

Back

Shading above a line indicates that the solutions to the inequality are all the points where the y-value is greater than the line.

Front

What does shading below a line in a graph indicate?

Back

Shading below a line indicates that the solutions to the inequality are all the points where the y-value is less than the line.

Front

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

Back

Substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all points (x, y) that satisfy the inequality.

Front

What does the inequality y ≤ -3x + 4 represent graphically?

Back

It represents a line with a solid line (because of ≤) and shading below the line, indicating all points where y is less than or equal to -3x + 4.