Graphing Linear Inequalities in Two Variables

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 (such as <, >, ≤, or ≥).

Front

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

Back

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

Front

What does the symbol '<' indicate in a linear inequality?

Back

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

Front

What type of line is used to represent 'y < mx + b'?

Back

A dashed line is used to represent 'y < mx + b' because the points on the line are not included in the solution set.

Front

What type of line is used to represent 'y ≤ mx + b'?

Back

A solid line is used to represent 'y ≤ mx + b' because the points on the line are included in the solution set.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid or dashed line. 2. Choose a test point not on the line to determine which side of the line to shade.

Front

What does the solution set of a linear inequality represent?

Back

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

Front

How can you determine if a point is part of the solution set for an inequality?

Back

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

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

Front

What is the significance of the y-intercept in a linear inequality?

Back

The y-intercept is the point where the line crosses the y-axis, and it helps in graphing the inequality.