6.4 Graphing Linear inequalities in two variables

Front

What is a linear inequality in two variables?

Back

A linear inequality in two variables is an inequality that can be expressed in the form ax + by < c, ax + by ≤ c, ax + by > c, or ax + by ≥ c, where a, b, and c are constants.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, 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 simultaneously.

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 in the system. If the point satisfies all inequalities, it is a solution.

Front

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

Back

The boundary line represents the points where the inequality changes from true to false. Points on the line are included if the inequality is ≤ or ≥, and excluded if it is < or >.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (≤, ≥) include the boundary line.

Front

What does the solution set of a system of inequalities represent?

Back

The solution set represents all the points in the coordinate plane that satisfy all inequalities in the system.

Front

How do you identify the solution set for a system of inequalities graphically?

Back

The solution set is identified by the overlapping shaded regions of the inequalities when graphed on the same coordinate plane.

Front

What is the role of test points in graphing inequalities?

Back

Test points are used to determine which side of the boundary line to shade. If the test point satisfies the inequality, shade the region containing that point.

Front

What is the importance of matching systems of inequalities to their graphs?

Back

Matching systems of inequalities to their graphs helps in visualizing the solution sets and understanding how different inequalities interact in the coordinate plane.