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 based on 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 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 is not on the line) and substituting it into the inequality. If the inequality holds true, shade that side; if not, shade the opposite side.

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 typically written as 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 < 2x + 3 represent graphically?

Back

The inequality y < 2x + 3 represents the region below the line y = 2x + 3, excluding the line itself.

Tags

CCSS.HSA.REI.D.12

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

Front

What is the intercept form of a linear inequality?

Back

The intercept form of a linear inequality is expressed as y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.HSA.REI.D.12