Exploring Proportional Relationships through Graphing

This video tutorial covers the concept of proportional relationships and how to graph them. It explains how to identify proportional relationships on a graph by checking if the points form a straight line through the origin. The tutorial also discusses how to find the constant of proportionality using ordered pairs. Several examples are provided to illustrate these concepts, and the video concludes with a discussion on the practical application of proportional relationships.

What is a key characteristic of a proportional relationship on a graph?

• It forms a curved line.

• It forms a zigzag pattern.

• It forms a straight line through the origin.

• It forms a straight line that does not pass through the origin.

How can you use a graph to find the constant of proportionality?

• By subtracting the x-value from the y-value.

• By finding the slope of the line.

• By adding the x and y values of an ordered pair.

• By dividing the y-value by the x-value of an ordered pair.

How do you calculate the constant of proportionality from an ordered pair?

• Add the x-value to the y-value.

• Subtract the x-value from the y-value.

• Divide the y-value by the x-value.

• Multiply the x-value by the y-value.

What is the formula for finding the constant of proportionality?

• x / y

• y / x

• x + y

• x - y

In the first example, why is the relationship not proportional?

• The points do not form a straight line.

• The points form a zigzag pattern.

• The points form a straight line but do not pass through the origin.

• The points form a curved line.

In the first example, what were the ordered pairs used to plot the points?

• (1, 3), (2, 6), (3, 9), (4, 12), (5, 15)

• (2, 6), (4, 8), (6, 10), (8, 12), (10, 14)

• (2, 6), (4, 12), (6, 18), (8, 24), (10, 30)

• (1, 2), (2, 4), (3, 6), (4, 8), (5, 10)

In the second example, what adjustment was made to the y-axis?

• The y-axis was labeled by fives.

• The y-axis was labeled by threes.

• The y-axis was labeled with odd numbers.

• The y-axis was labeled with even numbers.

Why was the second example considered proportional?

• The points formed a zigzag pattern.

• The points formed a straight line and passed through the origin.

• The points formed a straight line but did not pass through the origin.

• The points formed a curved line.

What does the constant of proportionality represent in the real-world example?

• The number of fathoms per foot.

• The number of feet per fathom.

• The number of feet per mile.

• The number of miles per fathom.

If the constant of proportionality is 6, what does it mean in terms of fathoms and feet?

• Six feet are one fathom.

• Six fathoms are one foot.

• One foot is 6 fathoms.

• One fathom is 6 feet.