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 graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shaded on one side of a boundary line.

Front

How do you determine which side of the line to shade in a linear inequality?

Back

To determine which side to shade, test a point not on the line (usually (0,0)). If it satisfies the inequality, shade that side; if not, shade the opposite side.

Front

What does the boundary line represent in a linear inequality?

Back

The boundary line represents the values where the inequality changes from true to false. If the inequality is strict (< or >), the line is dashed; if it is inclusive (≤ or ≥), the line is solid.

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 set (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Front

How do you graph the inequality y > 3x - 2?

Back

1. Graph the line y = 3x - 2 as a dashed line. 2. Choose a test point (e.g., (0,0)). 3. Since (0,0) does not satisfy the inequality, shade above the line.

Front

What does the inequality y ≤ -2x - 2 indicate about the shading?

Back

The inequality y ≤ -2x - 2 indicates that the region below the line y = -2x - 2 is shaded, including the line itself.

Front

If a point lies on the boundary line of an inequality, is it part of the solution set?

Back

Yes, if the boundary line is solid (for ≤ or ≥), the points on the line are part of the solution set.

Front

What is the solution set of the inequality y < 4x - 2?

Back

The solution set includes all points below the line y = 4x - 2, not including the line itself.

Front

How do you write the inequality for a graph that is shaded above a line?

Back

If the graph is shaded above a line, the inequality will typically be in the form y > mx + b or y ≥ mx + b.