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.

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.

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 >).

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.

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.

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.