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 (e.g., <, >, ≤, ≥).

Front

What does the solution set of a linear inequality represent?

Back

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

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line (solid for ≤ or ≥, dashed for < or >). 2. Shade the region that represents the solution set.

Front

What is the difference between a solid and dashed boundary line?

Back

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

Front

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

Back

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

Front

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

Back

The symbol '>' means that the value on the left is greater than the value on the right, excluding the boundary.

Front

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

Back

The symbol '<=' means that the value on the left is less than or equal to the value on the right, including the boundary.

Front

What is the first step in graphing a linear inequality?

Back

The first step is to graph the corresponding linear equation as a boundary line.

Front

What is the significance of the shading in the graph of a linear inequality?

Back

The shading indicates the region of the graph that contains all the solutions to the inequality.

Front

How do you know which side to shade when graphing a linear inequality?

Back

Choose a test point not on the boundary line (often (0,0) if it's not on the line) and substitute it into the inequality. Shade the side where the inequality holds true.