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 < 2?

Back

A dashed horizontal line is used to represent the inequality y < 2.

Front

What type of line is used to represent the inequality y ≤ 2?

Back

A solid horizontal line is used to represent the inequality y ≤ 2.

Front

How do you determine if a point is part of the solution set for a linear inequality?

Back

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

Front

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

Back

Shading above a line indicates that the solutions to the inequality are greater than the line (y > mx + b).

Front

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

Back

Shading below a line indicates that the solutions to the inequality are less than the line (y < mx + b).

Front

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

Back

A solid line indicates that the points on the line are included in the solution set (≤ or ≥), while a dashed line indicates that the points on the line are not included ( < or >).

Front

How do you graph the inequality y > -1/2 x + 5?

Back

To graph y > -1/2 x + 5, draw a dashed line for y = -1/2 x + 5 and shade above the line.