Graphing Linear Inequalities

Front

What does the inequality y ≥ -2x + 1 represent on a graph?

Back

The graph is a solid line, shaded above.

Front

How do you determine if a point is a solution to the inequality y ≤ 5x - 1?

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 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 (≥ or ≤), while a dotted line indicates they are not included (> or <).

Front

What does the inequality y > 3x - 2 mean in terms of graphing?

Back

The graph will have a dotted line for y = 3x - 2, and the area above the line will be shaded.

Front

Which inequality is equivalent to 3x - y > 4?

Back

y < 3x - 4.

Front

How can you tell which side of the line to shade when graphing an inequality?

Back

Choose a test point not on the line (usually (0,0) if it's not on the line) and substitute it into the inequality. If the inequality is true, shade that side.

Front

What does the inequality y < 3x + 2 represent on a graph?

Back

The graph will have a dotted line for y = 3x + 2, and the area below the line will be shaded.

Front

What is a solution set in the context of linear inequalities?

Back

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

Front

How do you graph the inequality 3x - 2y < 10?

Back

First, graph the line 3x - 2y = 10 as a dotted line, then shade below the line.

Front

What does it mean if a point (1, 7) is not a solution for the inequality y ≤ 5x - 1?

Back

It means that when you substitute x = 1 and y = 7 into the inequality, it does not hold true.