Linear Inequalities Test pt 3

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 (>, <, ≥, ≤).

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed line (for < or >) or a solid line (for ≤ or ≥). Then, shade the region that satisfies the inequality.

Front

What does the solution of a system of inequalities represent?

Back

The solution of a system of inequalities represents all the points that satisfy all inequalities in the system simultaneously.

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

Front

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

Back

Choose a test point not on the line (commonly (0,0)). Substitute it into the inequality. If the inequality holds true, shade the side containing the test point; otherwise, shade the opposite side.

Front

What is the graphical representation of the inequality y < 2?

Back

The graph is a horizontal line at y=2, with the area below the line shaded.

Front

What does the inequality y > 2x - 4 represent graphically?

Back

It represents a region above the line y = 2x - 4, which has a dashed line since the inequality is strict (>) and does not include the line itself.

Front

How can you solve a system of inequalities by graphing?

Back

Graph each inequality on the same coordinate plane, then identify the overlapping shaded region, which represents the solution set.

Front

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

Back

The intersection represents the set of solutions that satisfy both inequalities simultaneously.

Front

What does the inequality y ≤ 2x - 1 indicate about the line y = 2x - 1?

Back

It indicates that the line is solid (included in the solution) and the area below the line is shaded.