Redo: Graphing Linear Inequalities

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

How do you graph a linear inequality?

Back

1. Start by graphing the corresponding linear equation as a dashed or solid line. 2. Use a dashed line for < or > (not including the line) and a solid line for ≤ or ≥ (including the line). 3. Shade the region that satisfies the inequality: above the line for > or ≥, and below the line for < or ≤.

Front

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

Back

The symbol '>' means 'greater than'. It indicates that the values of the variable(s) must be greater than the value on the other side of the inequality.

Front

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

Back

The symbol '<' means 'less than'. It indicates that the values of the variable(s) must be less than the value on the other side of the inequality.

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(s) can be greater than or equal to the value on the other side of the inequality.

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(s) can be less than or equal to the value on the other side of the inequality.

Front

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

Back

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

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 (for ≤ or ≥). A dashed line indicates that points on the line are not included in the solution (for < or >).

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. It is represented graphically as a shaded region on the coordinate plane.

Front

How do you write an inequality from a graph?

Back

To write an inequality from a graph, identify the boundary line and determine if it is solid or dashed. Then, observe which side of the line is shaded to determine the direction of the inequality (greater than or less than).