Graphing Linear Inequalities Flashcard

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

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

Back

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

Front

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

Back

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

Front

How do you determine if a point is a solution to a linear inequality?

Back

Substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What does the inequality y ≥ -3/4 x + 3 indicate about the graph?

Back

It indicates that the region above the line (including the line itself) is part of the solution set.

Front

What is the solution set of an inequality?

Back

The solution set is the set of all points (x, y) that satisfy the inequality.

Front

How can you tell if a point is not part of the solution set for an inequality?

Back

If substituting the point into the inequality does not satisfy the condition, then it is not part of the solution set.

Front

What does the inequality y < 2x + 3 mean in terms of graphing?

Back

It means that the region below the line y = 2x + 3 is part of the solution set, and the line itself is not included.

Front

What is the significance of the slope in a linear inequality?

Back

The slope indicates the steepness of the line and the direction of the inequality (positive slope means the line rises, negative slope means it falls).

Front

What is the first step in graphing a linear inequality?

Back

The first step is to graph the corresponding linear equation as if it were an equality.