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 boundary line. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Finally, shade the appropriate region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

Front

What does the shaded region in a graph of a linear inequality represent?

Back

The shaded region represents all the solutions to the inequality, indicating the set of points (x, y) that satisfy the inequality.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

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

Tags

CCSS.HSA.REI.D.12

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 selecting a test point not on the line (commonly (0,0) if it's not on the line) and substituting it into the inequality. If the inequality holds true, shade the side containing the test point.

Tags

CCSS.HSA.REI.D.12

Front

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.

Front

What does the inequality y < mx + b represent?

Back

The inequality y < mx + b represents all the points below the line y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

The slope (m) indicates the steepness and direction of the line. A positive slope means the line rises from left to right, while a negative slope means it falls.

Front

How do you convert a linear equation to an inequality?

Back

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

Front

What is the graphical representation of the inequality y ≥ 3x - 2?

Back

The graphical representation includes a solid line for y = 3x - 2 and the region above the line, indicating all points (x, y) where y is greater than or equal to 3x - 2.

Tags

CCSS.HSA.REI.D.12