Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

Front

How do you graph a linear inequality in two variables?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Finally, shade the appropriate region based on the inequality.

Front

What does a solid line indicate in the graph of a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set, meaning the inequality is ≤ or ≥.

Front

What does a dashed line indicate in the graph of a linear inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set, meaning the inequality is < or >.

Front

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

Back

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

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation represents a straight line and includes an equality (e.g., y = mx + b), while a linear inequality represents a region of solutions and includes an inequality (e.g., y < mx + b).

Front

What does the inequality 5 ≥ x represent on a graph?

Back

The inequality 5 ≥ x represents all points to the left of the vertical line x = 5, including the line itself.

Front

What is the significance of the boundary line in graphing linear inequalities?

Back

The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not.

Front

Can a linear inequality have more than one solution?

Back

Yes, a linear inequality typically has infinitely many solutions, represented by the shaded region of the graph.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.