Graphing Linear Inequality

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 (>, <, ≥, ≤).

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions to the inequality, showing the region of the coordinate plane that satisfies the inequality.

Front

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

Back

A solid line indicates that points on the line are included in the solution set (≥ 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

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

Front

What does the boundary line of a linear inequality represent?

Back

The boundary line represents the values where the inequality changes from true to false. It separates the solution set from non-solution set.

Front

What is the solution set of a linear inequality?

Back

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

Front

How do you graph a linear inequality in two variables?

Back

1. Graph the boundary line. 2. Use a solid or dashed line based on the inequality. 3. Shade the region that represents the solution set.

Front

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

Back

The symbol '≥' means 'greater than or equal to', indicating that the values on the boundary line are included in the solution set.

Front

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

Back

The symbol '≤' means 'less than or equal to', indicating that the values on the boundary line are included in the solution set.

Front

How can you write a linear inequality from a word problem?

Back

Identify the quantities involved, determine the relationship (greater than, less than), and express it using inequality symbols.