Non-Proportional Relationships and Characteristics

The video tutorial explores non-proportional relationships, focusing on linear equations in the form y = mx + b. It explains the difference between proportional and non-proportional relationships, emphasizing the role of the y-intercept. Through examples like movie ticket purchases, fair parking, and dog growth, the tutorial illustrates how these relationships are represented in equations, tables, and graphs. The key takeaway is understanding the additive nature of non-proportional relationships compared to the multiplicative nature of proportional ones.

What is a key characteristic of non-proportional relationships?

• They include an additive component.

• They have a constant ratio of Y over X.

• They always pass through the origin.

• They can be represented by the equation y = kx.

In the equation y = mx + b, what does 'b' represent?

• The rate of change

• The y-intercept

• The constant of proportionality

• The slope

How does the equation y = mx + b differ from y = kx?

• y = mx + b includes a multiplicative component.

• y = mx + b includes an additive component.

• y = mx + b is used for proportional relationships.

• y = mx + b does not have a y-intercept.

In the movie ticket example, what is the role of the $3 fee?

• It is the constant of proportionality.

• It is the y-intercept.

• It is the slope.

• It is the rate of change.

Why does the graph of the movie ticket example not pass through the origin?

• Because the rate of change is zero.

• Because the y-intercept is zero.

• Because there is a service fee.

• Because the slope is negative.

In the parking and ride cost example, what is the equation for the total cost?

• y = 2x

• y = 10x

• y = 2x + 10

• y = 10x + 2

What makes the parking and ride cost example non-proportional?

• The absence of a y-intercept

• The presence of a multiplicative relationship

• The presence of an additive component

• The constant ratio of Y over X

In the German Shepherd example, what is the initial weight of the puppy?

• Two pounds

• Five pounds

• Three pounds

• Nine pounds

What is the rate of change in the German Shepherd example?

• Two pounds per week

• Nine pounds per week

• Three pounds per week

• Five pounds per week

Why is the German Shepherd's weight gain example considered non-proportional?

• Because it includes a multiplicative relationship

• Because it starts at zero weight

• Because it starts with an initial weight

• Because it has a constant ratio of Y over X