Understanding Non-Proportional Relationships

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 additive nature of the latter. Through examples like movie ticket purchases, fair parking, and German Shepherd growth, the tutorial illustrates how these relationships work, highlighting the role of the y-intercept and the rate of change.

What distinguishes a non-proportional relationship from a proportional one?

• It always passes through the origin.

• It includes an additive constant in the equation.

• It can be expressed as y = kx.

• It has a constant ratio of y over x.

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

• The rate of change

• The y-intercept

• The constant of proportionality

• The dependent variable

What role does 'b' play in the equation y = mx + b?

• It is the slope of the line.

• It represents the rate of change.

• It is the y-intercept.

• It is the independent variable.

In the movie ticket example, what does the $3 service fee represent?

• The y-intercept

• The rate of change

• The slope of the line

• The independent variable

Why is the relationship in the movie ticket example non-proportional?

• It has a constant ratio of y over x.

• It passes through the origin.

• It includes a multiplicative constant.

• It has an additive constant.

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

• y = 10x + 2

• y = 2x + 10

• y = 2x

• y = 10x

What makes the parking fee example a non-proportional relationship?

• It passes through the origin.

• It includes an additive constant.

• It has a constant ratio of y over x.

• It has a multiplicative constant.

In the German Shepherd example, what does the initial weight of 3 pounds represent?

• The slope of the line

• The rate of change

• The y-intercept

• The independent variable

How is the rate of change represented in the German Shepherd example?

• By the initial weight

• By the number of weeks

• By the weekly weight gain

• By the total weight

What is the equation for the German Shepherd's weight gain over time?

• y = 3x + 2

• y = 2x + 3

• y = 2x

• y = 3x