Graphing Inequalities in Two Variables

Front

What is an inequality in two variables?

Back

An inequality in two variables is a mathematical statement that compares two expressions using inequality symbols (>, <, ≥, ≤) and involves two variables, typically x and y.

Front

What does the graph of an inequality represent?

Back

The graph of an inequality represents all the possible solutions to that inequality, showing the region of the coordinate plane where the inequality holds true.

Front

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

Back

To determine if a point is a solution to an inequality, substitute the coordinates of the point into the inequality. If the inequality holds true, the point is part of the solution set.

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 set (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Front

What does the inequality y > -2 represent on a graph?

Back

The inequality y > -2 represents all points above the horizontal line y = -2, not including the line itself.

Front

How do you graph the inequality y ≤ 3/4x + 5?

Back

To graph y ≤ 3/4x + 5, first graph the line y = 3/4x + 5 as a solid line, then shade below the line to indicate that all points on or below the line are included in the solution set.

Front

What is the solution set of the inequality x > -2?

Back

The solution set of the inequality x > -2 includes all points to the right of the vertical line x = -2, not including the line itself.

Front

What does the inequality y < x - 3 represent?

Back

The inequality y < x - 3 represents all points below the line y = x - 3, not including the line itself.

Front

How can you tell which region to shade when graphing an inequality?

Back

To determine which region to shade, you can test a point not on the boundary line (often (0,0) if it's not on the line) in the inequality. If the inequality is true, shade that region; if false, shade the opposite region.

Front

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

Back

The boundary line separates the coordinate plane into two regions: one that satisfies the inequality and one that does not. The type of line (solid or dashed) indicates whether points on the line are included in the solution.