Exploring Linear Inequalities

Mr. Newman introduces linear inequalities, focusing on graphing and analyzing them. He explains how to determine which side of the graph to shade and how to verify solutions both graphically and algebraically. The tutorial includes a step-by-step guide to graphing inequalities and concludes with a practical word problem application involving budgeting for a party.

What does a dashed line on a graph of an inequality indicate?

• The inequality does not include the boundary line.

• The inequality includes the boundary line.

• The inequality is only valid in the positive quadrant.

• The inequality represents an equation, not an inequality.

If a point is on the shaded side of the graph, what does it signify?

• The point has no significance.

• The point represents the maximum value.

• The point is a solution to the inequality.

• The point is not a solution to the inequality.

What is the significance of a solid line in the graph of an inequality?

• It indicates that the inequality does not include the boundary line.

• It indicates that the inequality includes the boundary line.

• It is used only for decoration.

• It indicates an error in graphing.

What method can be used to check if a point is a solution to the inequality?

• Guessing based on the proximity to the line.

• Plugging the point into the inequality to see if it holds true.

• Checking if the point is below the line.

• Checking if the point is above the line.

How does one verify graphically if a point is a solution to the inequality?

• By checking if the point lies in the non-shaded region.

• By checking if the point lies on the line.

• By checking if the point lies in the shaded region.

• By checking if the point is at the origin.

How do you determine which side of the line to shade when graphing an inequality?

• Always shade below the line.

• Shade the side opposite to where the origin (0,0) falls after testing.

• Shade the side where the line is dashed.

• Always shade above the line.

Why is it important to understand whether the line is dashed or solid in graphing inequalities?

• To make the graph visually appealing.

• To understand which points are included in the solution set.

• To decide the type of graph to use.

• To determine the mathematical operations involved.

What does the inequality 2x + 0.75y ≤ 825 represent in a practical context?

• The maximum number of items one can buy.

• The minimum cost of items.

• The maximum cost Elijah can spend on items.

• The exact amount to be spent on items.

In the context of the problem, what does a point (2, 4) represent?

• Two bags of grapes and four packages of carrots.

• Two packages of carrots and four bags of grapes.

• Four bags of grapes and two packages of carrots.

• Four packages of carrots and two bags of grapes.

What does the inequality sign in 2x + 0.75y ≤ 825 indicate about Elijah's spending?

• He should not spend anything.

• He can spend up to 825.

• He must spend less than 825.

• He must spend more than 825.