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

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the appropriate region based on the inequality symbol.

Front

What does a dashed line indicate in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set (used for < or >).

Front

What does a solid line indicate in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set (used for ≤ 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 do you determine which side to shade when graphing a linear inequality?

Back

To determine which side to shade, pick a test point not on the line (often (0,0)) and substitute it into the inequality. If the inequality holds true, shade that side.

Front

What is the difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' uses a dashed line and does not include the line in the solution, while 'y ≤ mx + b' uses a solid line and includes the line.

Front

What does the inequality 'y > 2x + 3' represent graphically?

Back

It represents the region above the line y = 2x + 3, with a dashed line indicating that points on the line are not included.

Front

What is the significance of the slope in a linear inequality?

Back

The slope indicates the steepness of the line and the direction of the inequality (positive slope means the line rises, negative slope means it falls).

Front

How can you check if a point is a solution to a linear inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is a solution.