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 ≥) instead of an equal sign.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, depending on whether the inequality is strict (< or >) or inclusive (≤ or ≥). Then, shade the appropriate region of the graph that satisfies the inequality.

Front

What does it mean if a graph is shaded above the line?

Back

If a graph is shaded above the line, it indicates that the solutions to the inequality are all the points above the line, meaning the inequality is of the form y > mx + b or y ≥ mx + b.

Front

What does it mean if a graph is shaded below the line?

Back

If a graph is shaded below the line, it indicates that the solutions to the inequality are all the points below the line, meaning the inequality is of the form y < mx + b or y ≤ mx + b.

Front

What is the significance of a dashed line in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set of the inequality, which is the case for strict inequalities (< or >).

Front

What is the significance of a solid line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set of the inequality, which is the case for inclusive inequalities (≤ or ≥).

Front

How do you determine which side of the line to shade for an inequality?

Back

To determine which side of the line to shade, you can test a point not on the line (commonly the origin (0,0) if it is not on the line) in the inequality. If the inequality holds true, shade the side containing that point; otherwise, shade the opposite side.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you convert a linear inequality into slope-intercept form?

Back

To convert a linear inequality into slope-intercept form, isolate y on one side of the inequality, resulting in an expression of the form y < mx + b or y > mx + b.

Front

What is the relationship between the slope of a line and the direction of shading in a linear inequality?

Back

The slope of a line indicates the steepness and direction of the line. If the slope is positive, the shading will be above the line for greater than inequalities (y > mx + b). If the slope is negative, the shading will be below the line for less than inequalities (y < mx + b).