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 (>, <, ≥, ≤).

Front

How do you graph a linear inequality?

Back

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

Front

What does the solution to a system of inequalities represent?

Back

The solution to 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 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 point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the significance of the shaded region in the graph of a linear inequality?

Back

The shaded region represents all the possible solutions to the inequality, indicating where the inequality holds true.

Front

What does the inequality y < 2x + 3 represent graphically?

Back

It represents the area below the line y = 2x + 3, excluding the line itself.

Front

How do you solve a system of inequalities by graphing?

Back

Graph each inequality on the same coordinate plane, identify the shaded regions, and find the overlapping area which represents the solution.

Front

What is the solution set of the inequalities x > 1 and y < 2?

Back

The solution set is the region in the coordinate plane where x is greater than 1 and y is less than 2.

Front

What does the notation y ≥ mx + b indicate?

Back

It indicates that the line y = mx + b is included in the solution set, and the area above the line is shaded.