Linear Inequalities REVIEW

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 (e.g., <, >, ≤, ≥).

Front

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

Back

'≤' means 'less than or equal to', indicating that the value can be less than or equal to the expression.

Front

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

Back

'≥' means 'greater than or equal to', indicating that the value can be greater than or equal to the expression.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (for ≤ or ≥) or 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 they are not included (< or >).

Front

What does the solution set of a linear inequality represent?

Back

The solution set represents all the points (x, y) that satisfy the inequality.

Front

How can 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)). 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 convert a linear inequality into 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.

Front

What is the significance of the y-intercept in a linear inequality?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x = 0.