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Dependent & independent variables: equation

Video transcript
Let's see. We have this graph over here with t is the independent variable on the horizontal axis and d is the dependent variable on the vertical axis. And then they have a table here. Looks like this table corresponds to this graph. When t equals 1, d is 40, when t is equal to 2, d is 80. So these points correspond to points on this line. And then they explain to us, you are buying a gym membership. The membership costs $40 per month. In the graph and table above, d is the total number of dollars that you pay for your gym membership, so that's d right over there, and t is the time in months that you keep the membership. Write an equation for the amount of money d that you pay for your gym membership, if you keep the membership for t months. And you see that here. If you're one month, you pay $40, two months you pay another $40, you pay $80. You see that in the graph right over here. If you have 0 months, you pay nothing. Then one month, $40, the next month another $40 getting you to $80. So if I were to write this as an equation, the dependent variable here is the amount that I pay in dollars. So that is going to depend on the time. And how is it going to depend on the time in months? Well I'm going to pay $40 per month times the number of months. So I can either write it as 40 with a little asterisk sign, which is Shift 8-- and then I put t there-- or I could literally put just a t right over there. And I think that's right, because if my time is 0 according to this table and according to this graph, I pay nothing. If there was some initial membership charge then maybe we would add that membership charge and you would pay the monthly fee after that. But here this looks about right, that the dollars paid is equal to 40 times the time in months. The time in months is the independent variable. It drives the dependent variable, the number of dollars you pay.