Graphing Linear Inequality

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 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 the symbol '≥' indicate in a linear inequality?

Back

The symbol '≥' indicates that the values of the variable are greater than or equal to the value on the other side of the inequality.

Front

What does the symbol '≤' indicate in a linear inequality?

Back

The symbol '≤' indicates that the values of the variable are less than or equal to the value on the other side of the inequality.

Front

What is the significance of the slope in a linear inequality?

Back

The slope in a linear inequality indicates the steepness of the line and the direction of the relationship between the variables. A positive slope means that as one variable increases, the other also increases.

Front

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

Back

To determine which side of the line to shade, pick a test point not on the line (commonly (0,0) if it is not on the line) and substitute its coordinates into the inequality. If the inequality holds true, shade the side containing the test point.

Front

What is the difference between a dashed line and a solid line in graphing linear inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set (used for < or >), while a solid line indicates that the points on the line are included in the solution set (used for ≤ or ≥).

Front

What is the standard form of a linear inequality?

Back

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

Front

How can you convert a linear equation to a linear inequality?

Back

To convert a linear equation to a linear inequality, replace the equality sign (=) with an inequality sign (<, >, ≤, or ≥) based on the context of the problem.

Front

What is the role of the y-intercept in graphing linear inequalities?

Back

The y-intercept is the point where the line crosses the y-axis and is used to plot the line when graphing the corresponding linear equation.