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 '≥' 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

How do you graph the inequality y ≥ -2?

Back

To graph y ≥ -2, draw a horizontal line at y = -2 and shade the area above the line.

Front

How do you graph the inequality y < -1/2x + 3?

Back

To graph y < -1/2x + 3, draw a dashed line for y = -1/2x + 3 and shade the area below 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 (≥ or ≤), while a dashed line indicates they are not included (> or <).

Front

What does the inequality x ≥ -2 represent on a number line?

Back

It represents all numbers to the right of -2, including -2 itself.

Front

How do you determine which side of the line to shade when graphing an inequality?

Back

You can test a point not on the line (like (0,0)) in the inequality. If it satisfies the inequality, shade the side containing that point.

Front

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

Back

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

Front

How do you find the slope from the inequality y ≤ -1/2x + 3?

Back

The slope is -1/2, which indicates the line falls as you move from left to right.