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 written 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 symbol '<' represent in a linear inequality?

Back

The symbol '<' indicates that the values of the expression on the left are less than the value on the right.

Front

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

Back

The symbol '>' indicates that the values of the expression on the left are greater than the value on the right.

Front

What type of line is used to represent the inequality y < 2x + 3?

Back

A dashed line is used to represent the inequality y < 2x + 3 because the inequality does not include equality.

Front

What does shading above a line in a graph of a linear inequality indicate?

Back

Shading above the line indicates that the solutions to the inequality are all the points above the line.

Front

What does shading below a line in a graph of a linear inequality indicate?

Back

Shading below the line indicates that the solutions to the inequality are all the points below the line.

Front

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

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What type of line is used for the inequalities '≤' and '≥'?

Back

A solid line is used for the inequalities '≤' and '≥' because these inequalities include equality.

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 does the inequality x < 2 represent on a graph?

Back

The inequality x < 2 represents all points to the left of the vertical line x = 2, not including the line itself.