Graph Linear Inequalities In Two Variables

Front

What is a linear inequality in two variables?

Back

A linear inequality in two variables is an inequality that can be expressed in the form ax + by < c, ax + by > c, ax + by ≤ c, or ax + by ≥ c, where a, b, and c are constants.

Front

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

Back

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

Front

What is the difference between a solid line and a dotted line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution set (≤ or ≥), while a dotted line indicates that points on the line are not included ( < 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 does the inequality symbol '>' indicate about the relationship between two expressions?

Back

The symbol '>' indicates that the expression on the left is greater than the expression on the right.

Front

What does the inequality symbol '<' indicate about the relationship between two expressions?

Back

The symbol '<' indicates that the expression on the left is less than the expression on the right.

Front

What is the significance of the inequality symbols '≤' and '≥'?

Back

The symbols '≤' and '≥' indicate that the values on the left can be equal to the values on the right, in addition to being less than or greater than.

Front

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

Back

Graph the line y = 2x + 3 as a dotted line and shade the region below the line.

Front

What is the first step in graphing a linear inequality?

Back

The first step is to graph the corresponding linear equation as either a solid or dotted line.

Front

What does it mean if a point lies on the line of a linear inequality?

Back

If a point lies on the line, it is a solution only if the line is solid (for ≤ or ≥). If the line is dotted, the point is not included in the solution set.