Graphing Systems of Linear Inequalities (Part 3)

Front

What is a linear inequality?

Back

A linear inequality is a mathematical expression that relates a linear function to a value using inequality symbols (such as <, >, ≤, or ≥) instead of an equal sign.

Front

How do you graph a linear inequality?

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 region that satisfies the inequality.

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the shaded region of the graph.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

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

Front

How can you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the significance of the intersection of shaded regions in a graph of inequalities?

Back

The intersection of shaded regions represents the set of solutions that satisfy all inequalities in the system.

Front

What does the notation 'y ≤ 2x - 1' represent?

Back

This notation represents a linear inequality where the values of y are less than or equal to the values of the linear function 2x - 1.

Front

How do you solve a system of inequalities by graphing?

Back

To solve a system of inequalities by graphing, graph each inequality on the same coordinate plane, shade the appropriate regions, and identify the intersection of the shaded areas.

Front

What is the role of the boundary line in graphing inequalities?

Back

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

Front

What does the inequality 'y > -2x + 3' indicate about the graph?

Back

The inequality 'y > -2x + 3' indicates that the region above the line y = -2x + 3 is included in the solution set.