Linear inequalities (two variables) 12.3.24

Front

What is a linear inequality in two variables?

Back

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

The symbol '≤' means 'less than or equal to', indicating that the values of the variable can be equal to the boundary line or less than it.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

The symbol '≥' means 'greater than or equal to', indicating that the values of the variable can be equal to the boundary line or greater than it.

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line represents the values where the inequality changes from true to false. It divides the graph into two regions: one that satisfies the inequality and one that does not.

Tags

CCSS.HSA.REI.D.12

Front

How do you determine which side of the boundary line to shade?

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.

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 by the shaded region on the graph.

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

Tags

CCSS.HSA.REI.D.12

Front

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

Back

Front

What does it mean if a graph of a linear inequality is shaded above the line?

Back

Tags

CCSS.HSA.REI.D.12