Identify Proportional Relationships by Examining the Origin

This lesson explains how to identify proportional relationships by exploring the concept of the origin. It covers the definition of proportions, the coordinate plane, and examples using Amy's and Al's dog walking businesses. Amy's business is used to illustrate a proportional relationship, while Al's business demonstrates a non-proportional relationship due to the additional fee. The lesson emphasizes that proportional relationships must be linear and pass through the origin, addressing common misunderstandings.

What is the significance of the origin in a coordinate plane?

• It is the highest point on the graph.

• It is the point where the graph ends.

• It is the point where the axes intersect.

• It is the midpoint of the graph.

Which of the following is a characteristic of a proportional relationship?

• It never passes through the origin.

• It has a constant addition factor.

• It always passes through the origin.

• It forms a curved line on a graph.

In Amy's dog walking business, what does the $8 per walk represent?

• The total earnings for the day.

• The fee for signing up.

• The rate of earnings per walk.

• The cost of dog food.

How can you determine if a relationship is proportional using a graph?

• The graph should be a curved line and not pass through the origin.

• The graph should be a straight line and not pass through the origin.

• The graph should be a curved line and pass through the origin.

• The graph should be a straight line and pass through the origin.

Why is Al's dog walking business not considered a proportional relationship?

• It forms a straight line on the graph.

• It has a constant rate per walk.

• It does not involve any fees.

• It includes an additional fee that prevents it from passing through the origin.

What is a common misunderstanding about proportional relationships?

• They must always be non-linear.

• They do not need to pass through the origin.

• They can include addition and still be proportional.

• They must be linear and pass through the origin.

What is the key difference between Amy's and Al's business models in terms of proportionality?

• Amy's model includes a sign-up fee.

• Both models are proportional.

• Al's model is linear and passes through the origin.

• Amy's model is proportional, while Al's is not due to the additional fee.