Graphing Linear Inequalities 2024

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 ≥). It represents a region of the coordinate plane.

Front

What does the symbol '≤' mean in a linear inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the values of the variable can be less than or equal to a certain number.

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the values of the variable can be greater than or equal to a certain number.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a dashed line (for < or >) or a solid line (for ≤ or ≥). 2. Shade the region that satisfies the inequality.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all ordered pairs (x, y) that make the inequality true.

Front

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

Back

A solid line indicates that points on the line are included in the solution (≤ or ≥), while a dashed 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

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

Front

What is the standard form of a linear inequality?

Back

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

Front

How can you write an inequality from a word problem?

Back

Identify the quantities involved, determine the relationship (greater than, less than, etc.), and express it using variables and an inequality symbol.

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. It helps in graphing the inequality and understanding the relationship between x and y.