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 (like <, >, ≤, or ≥) and involves two variables, typically x and y.

Front

What does the solution set of an inequality represent?

Back

The solution set of an inequality represents all the ordered pairs (x, y) that satisfy the inequality.

Front

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

Back

To graph y < x - 3, first graph the line y = x - 3 as a dashed line (since it's a strict inequality). Then shade the region below the line, indicating all points where y is less than x - 3.

Front

What type of line is used for inequalities with < or >?

Back

A dashed or dotted line is used for inequalities with < or > to indicate that points on the line are not included in the solution set.

Front

What type of line is used for inequalities with ≤ or ≥?

Back

A solid line is used for inequalities with ≤ or ≥ to indicate that points on the line are included in the solution set.

Front

How can you determine if a point is part of the solution set for an inequality?

Back

To determine if a point is part of the solution set, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is part of the solution set.

Front

What does the graph of an inequality in two variables look like?

Back

The graph of an inequality in two variables consists of a line (solid or dashed) and a shaded region that represents all the solutions to the inequality.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary line, while a non-strict inequality (≤ or ≥) includes the boundary line.

Front

How do you identify the boundary line of an inequality?

Back

The boundary line of an inequality is identified by rewriting the inequality as an equation (e.g., y = mx + b) and graphing that line.

Front

What does shading above the line indicate in a graph of an inequality?

Back

Shading above the line indicates that the solutions to the inequality are all the points where y is greater than the value of the line at that x.