Graphing Linear Inequalities

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 (e.g., <, >, ≤, ≥).

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shown as a shaded region on one side of a boundary line.

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

How do you determine the boundary line for a linear inequality?

Back

To determine the boundary line, convert the inequality to an equation (replace the inequality sign with an equals sign) and graph that line.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to,' indicating that the value can be greater than or equal to a certain number.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than,' indicating that the value must be smaller than a certain number.

Front

How can you tell 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, the point is a solution.

Front

What is the solution set of an inequality?

Back

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

Front

What does it mean if a point lies on the boundary line of a graph of an inequality?

Back

If a point lies on the boundary line of a graph of an inequality with a solid line, it is part of the solution set; if it lies on a dashed line, it is not part of the solution set.

Front

How do you graph the inequality y > 2x + 1?

Back

First, graph the line y = 2x + 1 with a dashed line. Then, shade the region above the line to represent all points where y is greater than 2x + 1.