Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '≤' mean in a linear inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left is either less than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (for ≥ or ≤) or a dashed line (for > or <). 2. Shade the region that satisfies the inequality.

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

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

Back

It represents the area below the line y = -3/4x + 3, not including the line itself.

Front

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

Back

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

Front

What is the solution set of the inequality x < -1?

Back

The solution set includes all real numbers less than -1, represented graphically as a line extending left from -1, not including -1.

Front

What does the inequality y ≥ 2/5x + 1 represent graphically?

Back

It represents the area above the line y = 2/5x + 1, including the line itself.

Front

What is the slope of the line represented by the equation y = -3/4x + 3?

Back

The slope is -3/4, indicating that for every 4 units moved to the right, the line moves down 3 units.