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.

Front

What does the symbol '>' indicate in an inequality?

Back

The symbol '>' indicates that the value on the left is greater than the value on the right.

Front

What does the symbol '<' indicate in an inequality?

Back

The symbol '<' indicates that the value on the left is less than the value on the right.

Front

What is the difference between a solid line and a dashed line when 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 do you determine which side of the line to shade when graphing a linear inequality?

Back

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

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 is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality, represented graphically as a shaded region on the coordinate plane.

Front

How can 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 does the inequality 'y > 3x - 2' represent graphically?

Back

The inequality 'y > 3x - 2' represents the region above the line y = 3x - 2, where the line itself is dashed, indicating that points on the line are not included in the solution.