Graphing Systems of 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 (>, <, ≥, ≤).

Front

How do you rewrite a linear inequality in 'y=' form?

Back

To rewrite a linear inequality in 'y=' form, isolate y on one side of the inequality. For example, from 3x - 6y > 12, you would rearrange it to y < (1/2)x - 2.

Front

What does the solution of a system of linear inequalities represent?

Back

The solution of a system of linear inequalities represents all the points (x, y) that satisfy all inequalities in the system.

Tags

CCSS.HSA.REI.D.12

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane, which is the area above or below the line defined by the corresponding linear equation.

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

Tags

CCSS.HSA.REI.D.12

Front

How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does it mean if a system of inequalities has no solution?

Back

A system of inequalities has no solution if the regions represented by the inequalities do not overlap, meaning there are no points that satisfy all inequalities.

Tags

CCSS.HSA.REI.D.12

Front

What does it mean if a system of inequalities has infinitely many solutions?

Back

A system of inequalities has infinitely many solutions if the inequalities overlap in such a way that there are countless points that satisfy all of them.

Tags

CCSS.HSA.REI.D.12

Front

How do you graph a system of linear inequalities?

Back

To graph a system of linear inequalities, graph each inequality on the same coordinate plane, shading the appropriate half-plane for each, and identify the region where all shaded areas overlap.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

The boundary line separates the coordinate plane into two regions: one that satisfies the inequality and one that does not.

Tags

CCSS.HSA.REI.D.12