Graph 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 written in the form ax + by < c, ax + by > c, ax + by ≤ c, or ax + by ≥ c, where a, b, and c are constants.

Front

What does the shaded region represent in a graph of a linear inequality?

Back

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

Front

What is the significance of a dotted line in the graph of a linear inequality?

Back

A dotted line indicates that the points on the line are not included in the solution set (i.e., the inequality is strict: < or >).

Front

What does a solid line indicate in the graph of a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set (i.e., the inequality is non-strict: ≤ or ≥).

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, then the point is a solution.

Front

What is the first step in graphing a linear inequality?

Back

The first step is to graph the corresponding linear equation (replace the inequality sign with an equal sign).

Front

What does the term 'solution set' refer to in the context of linear inequalities?

Back

The solution set refers to all the points (x, y) that satisfy the inequality.

Front

Which of the following points is part of the solution set for the inequality y > 2x + 1? (0, 3), (1, 2), (2, 5)

Back

(0, 3) is part of the solution set because it satisfies the inequality.

Front

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

Back

The boundary line separates the solution set from the non-solution set in the graph.

Front

How can you tell if a point lies in the shaded region of a graph?

Back

You can test the point by substituting its coordinates into the inequality. If the inequality is true, the point lies in the shaded region.