Proportional vs Non Proportional Relationships

The video tutorial explains proportional and non-proportional relationships, focusing on how to identify them in tables and graphs. It defines a proportional relationship as one where the ratio between two variables is constant. The video provides examples and practice exercises, showing how to determine proportionality in tables by checking if the ratio of y over x is consistent. It also explains that a proportional graph must be linear and pass through the origin. Additionally, the tutorial covers how to identify proportional situations from descriptions, emphasizing the importance of the ratio and the origin point.

What defines a proportional relationship between two variables?

• The product of the variables must increase linearly.

• The difference between the variables must remain constant.

• The variables must add up to the same total.

• The ratio between the variables must always be equal.

How can you determine if a table represents a proportional relationship?

• By verifying the table has at least three rows.

• By confirming the table contains only whole numbers.

• By checking if the ratio of y over x is constant across the table.

• By ensuring each row adds up to the same total.

What is a key feature of a proportional table?

• The ratio of corresponding x and y values must be constant.

• It should contain equal numbers of x and y values.

• It must start with the value zero.

• Each row must sum to the same total.

What indicates a non-proportional relationship in a table?

• If the ratio of y over x varies between rows.

• If the table has more than two columns.

• If the sum of each row is different.

• If the table includes negative numbers.

If a table's y over x ratio changes in different rows, how is the relationship classified?

• Non-proportional

• Proportional

• Linear

• Undefined

Which characteristics must a graph have to represent a proportional relationship?

• The graph must contain only positive values.

• The graph must be a curve that passes through the origin.

• The graph must be linear and include the point (0,0).

• The graph must intersect the y-axis above the origin.

Why is a graph that curves not considered proportional?

• Because it intersects the y-axis multiple times.

• Because it is not a straight line.

• Because it only contains positive values.

• Because it does not pass through the origin.

What does it mean if a graph is linear and passes through the origin?

• It represents a non-proportional relationship.

• It indicates a decreasing relationship.

• It signifies a proportional relationship.

• It suggests a quadratic relationship.

In a scenario where a product is sold for a fixed price per unit, is the relationship between the number of products sold and the total revenue proportional?

• Yes, because the ratio of total revenue over products sold remains constant.

• No, because the total revenue increases with each product sold.

• Yes, but only if more than one product is sold.

• No, because the price per product can vary.

In creating a table from a description, what is a crucial first step to determine proportionality?

• Ensuring the description involves money.

• Choosing a large enough sample size.

• Calculating the total sum of all values first.

• Starting with a zero value for both variables.