Graphing Linear Inequalites

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 '>' represent in inequalities?

Back

The symbol '>' means 'greater than'.

Front

What does the symbol '<' represent in inequalities?

Back

The symbol '<' means 'less than'.

Front

What does the symbol '≥' represent in inequalities?

Back

The symbol '≥' means 'greater than or equal to'.

Front

What does the symbol '≤' represent in inequalities?

Back

The symbol '≤' means 'less than or equal to'.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed line (for < or >) or solid line (for ≤ or ≥), then shade the appropriate region based on 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

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

Back

Choose a test point not on the line (commonly (0,0)). If the inequality is true for that point, shade the side of the line that includes the test point.

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

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.