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

'≥' means 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

'≤' means 'less than or equal to'.

Front

How do you graph the inequality y > -x - 5?

Back

1. Graph the line y = -x - 5 as a dashed line. 2. 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 they are not included (> or <).

Front

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

Back

Choose a test point not on the line (like (0,0)). Substitute it into the inequality. If true, shade the side containing the test point.

Front

What is the solution set of an inequality?

Back

The solution set is the set of all points that satisfy the inequality.

Front

How do you graph the inequality y < 2x - 5?

Back

1. Graph the line y = 2x - 5 as a dashed line. 2. Shade the area below the line.

Front

What does the inequality y ≥ -x + 1 represent graphically?

Back

It represents all points on or above the line y = -x + 1.

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.