Understanding Graphs and Equations for Gym Membership Costs

The video tutorial explains the relationship between time and cost in a gym membership scenario using a graph and table. It introduces the independent variable (time in months) and the dependent variable (cost in dollars). The tutorial derives an equation to calculate the total cost based on the number of months, validating it with examples. The cost is $40 per month, and the equation is d = 40t, where d is the total cost and t is the time in months.

What does the variable 't' represent in the graph?

• The time in months

• The total cost in dollars

• The number of gym visits

• The initial membership fee

In the gym membership scenario, what does 'd' stand for?

• The total cost in dollars

• The number of gym visits

• The initial membership fee

• The duration of the membership

How much do you pay for the gym membership if you have it for 2 months?

• $40

• $20

• $80

• $100

What is the equation for the total cost 'd' of the gym membership?

• d = 20 * t

• d = 40 * t

• d = 60 * t

• d = 80 * t

If you have the membership for 0 months, how much do you pay?

• $0

• $20

• $40

• $80

What would change in the equation if there was an initial membership charge?

• The equation would remain the same

• A constant would be added to the equation

• The multiplication factor would change

• The equation would become a division

Why is the time in months considered the independent variable?

• Because it determines the total cost

• Because it is not related to the cost

• Because it is the same as the dependent variable

• Because it is always constant

What happens to the total cost if the membership duration doubles?

• The cost triples

• The cost doubles

• The cost halves

• The cost remains the same

If the membership cost per month was $50 instead of $40, what would the new equation be?

• d = 50 * t

• d = 40 * t

• d = 60 * t

• d = 70 * t

What is the role of the dependent variable in this scenario?

• It is unrelated to the independent variable

• It determines the time in months

• It is driven by the independent variable

• It is always constant