Dependent and independent variables exercise: express the graph as an equation | Khan Academy

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.

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