6.4 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 (>, <, ≥, ≤) instead of an equal sign.

Front

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

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

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

Back

The symbol '≤' indicates that the value on the left is less than or equal to the value on the right.

Front

How do you graph a linear inequality with '>' or '<'?

Back

Use a dashed line to represent the boundary line, and shade the region that satisfies the inequality.

Front

How do you graph a linear inequality with '≥' or '≤'?

Back

Use a solid line to represent the boundary line, and 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 is the solution set of a linear inequality?

Back

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

Front

How can you determine the correct graph for a given linear inequality?

Back

Identify the type of line (solid or dashed) based on the inequality symbol, then shade the appropriate region based on the direction of the inequality.

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 convert a linear inequality to slope-intercept form?

Back

Isolate y on one side of the inequality to express it in the form y < mx + b or y > mx + b.