Graphing Linear Inequalities and Systems of 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 (>, <, ≥, ≤).

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 shown as a shaded region on a coordinate plane.

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 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

What does the inequality y ≤ 2x - 1 represent graphically?

Back

It represents the region below or on the line y = 2x - 1, including the line itself.

Front

What is a system of linear inequalities?

Back

A system of linear inequalities consists of two or more linear inequalities that are considered together, and the solution is the region where all inequalities overlap.

Front

How do you graph a system of linear inequalities?

Back

Graph each inequality on the same coordinate plane, shading the appropriate regions, and identify the overlapping shaded area as the solution.

Front

What does the inequality y > -2x + 3 represent?

Back

It represents the region above the line y = -2x + 3, not including the line itself.

Front

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

Back

The boundary line separates the solution set from the non-solution set; points on the line may or may not be included based on the inequality.

Front

How can you check if a point lies in the solution set of a system of inequalities?

Back

Substitute the point's coordinates into each inequality in the system. If it satisfies all inequalities, it lies in the solution set.