Understanding Proportional Relationships

The video tutorial explains the concept of slope as a proportion, focusing on direct variation and proportional relationships. It uses examples like gasoline cost, apple pricing, and a bike ride to illustrate how proportionality works in equations, tables, and graphs. The tutorial emphasizes that proportional graphs are linear and pass through the origin, distinguishing them from non-proportional graphs.

What is a proportional relationship?

• A relationship where quantities vary inversely.

• A relationship where quantities vary randomly.

• A relationship where quantities do not vary.

• A relationship where quantities vary directly.

What does the equation y = mx represent?

• A non-linear relationship.

• A quadratic relationship.

• A proportional relationship.

• An inverse relationship.

In the gasoline cost example, what is the unit rate?

• $12.72 per gallon

• $8.48 per gallon

• $0 per gallon

• $4.24 per gallon

What is the significance of the point (0,0) in a proportional graph?

• It indicates a non-proportional relationship.

• It represents the maximum value of the graph.

• It shows the starting point of a non-linear graph.

• It confirms the graph passes through the origin.

In the apple cost example, what is the constant rate of change?

• 40 cents per apple

• 5 dollars per apple

• 10 cents per apple

• 2 dollars per apple

How is the graph of the apple cost example structured?

• It is a horizontal line.

• It is a zigzag line.

• It is a curve.

• It is a straight line through the origin.

What is Sydney's bike ride unit rate?

• 60 miles per hour

• 12 miles per hour

• 24 miles per hour

• 120 miles per hour

What does the graph of Sydney's bike ride illustrate?

• A line that does not pass through the origin.

• A non-linear relationship.

• A proportional relationship with a curve.

• A straight line through the origin.

What makes a graph non-proportional?

• It is a straight line.

• It has a y-intercept other than zero.

• It is a horizontal line.

• It passes through the origin.