Proportional Relationships in Graphs

The video tutorial covers identifying proportional and non-proportional relationships in graphs. It explains the two key rules for proportional relationships: the line must be straight and pass through the origin. Examples are provided to illustrate these concepts, including a detailed analysis of candy bar sales to determine proportionality. The tutorial also demonstrates how to graph proportional relationships and analyze non-proportional graphs. The lesson concludes with a comparison of different graphs and a summary of key points.

What are the two key rules for determining if two quantities are proportional on a graph?

• The line is curved and passes through the origin.

• The line is curved and does not pass through the origin.

• The line is straight and passes through the origin.

• The line is straight and does not pass through the origin.

Which of the following is NOT an example of a proportional relationship on a graph?

• A straight line passing through the origin and extending infinitely.

• A straight line not passing through the origin.

• A curved line.

• A straight line passing through the origin.

In the candy bar example, why is the relationship not proportional?

• The number of candy bars sold varies.

• The cost per candy bar is constant.

• The cost per candy bar varies.

• The number of candy bars sold is constant.

In the candy bar example, what is the cost per bar when 5 bars are sold for $4?

• $1.50

• $2.00

• $1.25

• $0.80

How do you create an equivalent ratio for graphing proportional relationships?

• By keeping the y-values constant.

• By adding a constant to both x and y values.

• By multiplying both x and y values by the same factor.

• By keeping the x-values constant.

When graphing proportional relationships, what is the first step?

• Connect the points with a zigzag line.

• Plot the points randomly.

• Start at the origin and plot points based on the ratio.

• Draw a curved line through the points.

What is the significance of the origin in determining proportionality on a graph?

• The line must start at the origin but can curve.

• The line must pass through the origin to be proportional.

• The line must avoid the origin to be proportional.

• The line must curve around the origin to be proportional.

What happens to the points on a graph if the relationship is not proportional?

• All points form a perfect circle.

• Points form a zigzag pattern.

• Points deviate from a straight line through the origin.

• All points lie on a straight line through the origin.

Why is it important for the line to pass through the origin in a proportional relationship?

• It confirms the relationship is non-proportional.

• It makes the graph look symmetrical.

• It ensures the line is curved.

• It verifies the relationship is proportional.

In the second graph example, why is the relationship not proportional?

• The line is curved and does not pass through the origin.

• The line is curved and passes through the origin.

• The line is straight but does not pass through the origin.

• The line is straight and passes through the origin.