Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

Front

What does the symbol '>' mean in a linear inequality?

Back

The symbol '>' means 'greater than'. It indicates that the value on the left side of the inequality is larger than the value on the right side.

Tags

CCSS.6.EE.B.8

Front

What does the symbol '<' mean in a linear inequality?

Back

The symbol '<' means 'less than'. It indicates that the value on the left side of the inequality is smaller than the value on the right side.

Tags

CCSS.6.EE.B.8

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left side is either larger than or equal to the value on the right side.

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left side is either smaller than or equal to the value on the right side.

Tags

CCSS.6.EE.B.8

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, depending on whether the inequality is strict (< or >) or inclusive (≤ or ≥). Then shade the appropriate region based on the inequality.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

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

Tags

CCSS.HSA.REI.D.12

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)). Substitute the coordinates into the inequality. If the inequality holds true, shade the side containing the test point; otherwise, shade the opposite side.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

Front

How can you convert a linear inequality into slope-intercept form?

Back