Solutions to graphs 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

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 where the inequality holds true.

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of a dotted line in the graph of a linear inequality?

Back

A dotted line indicates that points on the line are not included in the solution set (for inequalities using < or >).

Tags

CCSS.HSA.REI.D.12

Front

What does a solid line indicate in the graph of a linear inequality?

Back

A solid line indicates that points on the line are included in the solution set (for inequalities using ≤ or ≥).

Tags

CCSS.HSA.REI.D.12

Front

How do you determine if a point is a solution to a linear inequality?

Back

Substitute the x and y coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the solution set of an inequality?

Back

The solution set is the set of all points (x, y) that satisfy the inequality.

Tags

CCSS.HSA.REI.D.12

Front

Is the point (2, 1) a solution to the inequality y > -x + 7?

Back

No, because when substituting (2, 1) into the inequality, it does not satisfy the condition.

Front

Which point is NOT part of the solution set for the inequality y < 2x + 3? (0, 0), (-10, -10), (-1, 5), (5, 20)

Back

(-10, -10) is NOT part of the solution set.

Front

Is the point (3, 2) a solution for the inequality y ≤ -x + 5?

Back

No, because it is not in the shaded region of the graph.

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

It means that the point is a solution if the line is solid (≤ or ≥) but not a solution if the line is dotted (< or >).

Tags

CCSS.HSA.REI.D.12