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?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Finally, shade the appropriate region based on the inequality.

Front

What does a solid line indicate in the graph of a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set, which occurs when the inequality symbol is ≤ or ≥.

Front

What does a dashed line indicate in the graph of a linear inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set, which occurs when the inequality symbol is < or >.

Front

How can you determine which side of the line to shade when graphing a linear inequality?

Back

You can determine which side to shade by testing a point not on the line (commonly (0,0)). If the point satisfies the inequality, shade the side containing that point; otherwise, shade the opposite side.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation states that two expressions are equal, while a linear inequality states that one expression is greater than or less than another, allowing for a range of solutions.

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What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

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

Back

To convert a linear inequality into slope-intercept form (y = mx + b), isolate y on one side of the inequality.

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 does the y-intercept represent in the context of a linear inequality?

Back

The y-intercept represents the point where the line crosses the y-axis, which is the value of y when x = 0.