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?

Back

'≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '≤' represent?

Back

'≤' means 'less than or equal to'. It indicates that the value on the left is either less than or equal to the value on the right.

Front

How do you graph the inequality y ≥ -3?

Back

To graph y ≥ -3, draw a horizontal line at y = -3. Use a solid line to indicate that points on the line are included, and 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 points on the line are included in the solution (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Front

How do you determine the solution set for the inequality y < 1/2x + 2?

Back

To determine the solution set, graph the line y = 1/2x + 2 with a dashed line, and shade the area below the line.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you identify the slope from the equation y = -2x - 1?

Back

In the equation y = -2x - 1, the slope (m) is -2.

Front

What does it mean if a graph represents the inequality y > 2x - 1?

Back

It means that the solution set includes all points above the line y = 2x - 1, and the line itself is dashed, indicating that points on the line are not included.

Front

How do you graph the inequality y ≤ -x - 4?

Back

To graph y ≤ -x - 4, draw a solid line for y = -x - 4 and shade the area below the line.