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 ≥).

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

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What does it mean if a graph is shaded above the line?

Back

If a graph is shaded above the line, it indicates that the solutions to the inequality are all the points above the line, typically representing inequalities with 'greater than' (>) or 'greater than or equal to' (≥).

Front

What does it mean if a graph is shaded below the line?

Back

If a graph is shaded below the line, it indicates that the solutions to the inequality are all the points below the line, typically representing inequalities with 'less than' (<) or 'less than or equal to' (≤).

Front

How do you graph the inequality y ≥ -3/4 x + 3?

Back

To graph y ≥ -3/4 x + 3, first graph the line y = -3/4 x + 3 with a solid line, then shade the region above the line.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line separates the solution set from the non-solution set. Points on the line may or may not be included in the solution set, depending on whether the inequality is strict or inclusive.

Front

What is the solution set of the inequality y < -2x + 5?

Back

The solution set includes all points below the line y = -2x + 5, not including the line itself.

Front

How can you tell which direction to shade when graphing an inequality?

Back

To determine the shading direction, consider the inequality symbol: shade above the line for 'greater than' (>) or 'greater than or equal to' (≥), and shade below the line for 'less than' (<) or 'less than or equal to' (≤).