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

Front

What does the shaded region in a graph of a linear inequality represent?

Back

The shaded region represents all the possible solutions to the inequality.

Front

What does a dotted line indicate in the graph of a linear inequality?

Back

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

Front

What does a solid line indicate in the graph of a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set (for inequalities using ≤ or ≥).

Front

How do you determine if a point is a solution to a linear inequality?

Back

Substitute the x and y coordinates of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the solution set of an inequality?

Back

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

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line separates the graph into two regions: one that contains the solutions and one that does not.

Front

How can you graph the inequality y < 2x + 3?

Back

First, graph the line y = 2x + 3 with a dotted line. Then shade the region below the line.

Front

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

Back

'y ≤ mx + b' includes the boundary line (solid line), while 'y < mx + b' does not include the boundary line (dotted line).

Front

Which point is a solution for the inequality y > -x + 1?

Back

Any point above the line y = -x + 1 is a solution.