Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

Front

How do you graph a linear inequality in two variables?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then, shade the region that satisfies the inequality.

Front

What does it mean if a line is dotted in a graph of a linear inequality?

Back

A dotted line indicates that the points on the line are not included in the solution set of the inequality.

Front

What does it mean if a line is solid in a graph of a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set of the inequality.

Front

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

Back

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

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. A positive slope means the line rises, while a negative slope means it falls.

Front

What is the y-intercept in the context of linear inequalities?

Back

The y-intercept is the point where the line crosses the y-axis, which can help in graphing the inequality.

Front

What does the inequality y < mx + b represent?

Back

This inequality represents all the points below the line defined by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (≤, ≥) do include the boundary line.

Front

How do you identify the solution set of a linear inequality graphically?

Back

The solution set is identified by the shaded region of the graph, which represents all the points that satisfy the inequality.