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## Algebra (all content)

### Course: Algebra (all content) > Unit 1

Lesson 7: Dependent & independent variables- Dependent & independent variables
- Dependent & independent variables: graphing
- Dependent & independent variables: equation
- Independent versus dependent variables
- Tables from equations with 2 variables
- Match equations to coordinates on a graph
- Relationships between quantities in equations

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# Dependent & independent variables: equation

We're flipping the last video on its head and doing the opposite. This time we give you the graph and ask you to express it as an equation. Created by Sal Khan.

## Want to join the conversation?

- What is an independent and dependent variable. This is confusing me(17 votes)
- independent variable is x and dependent variable is y. the y-variable is dependent on the x-variable for its answer(13 votes)

- What does the t stand for and why do we have to put it in our answer(5 votes)
- T does not have to stand for anything, yet T stands for Time in months Sal says so at0:30and we have to put it in the answer because otherwise we are just giving a number with no place where it goes.(6 votes)

- Can someone describe dependent and independent variables more clearly to me?

I think I get the gist, but if I stop thinking about it I forget.(2 votes)- The dependent variable (most commonly y) depends on the independent variable (most commonly x). You can put in a value for the independent variable (input) to get out a value for the dependent variable (output), so the y= form of an equation is the most common way of expressing a independent/dependent relationship. In many real world situations, your logical part of brain will correctly identify the dependent variable (does ice cream sales depend on the weather, or does the weather depend on ice cream sales? does the dog running away depend on the gate being open, or does the gate being open depend on the dog running away?).

In real world equations particularly in Science, any of the variables can be dependent such as if v = d/t, then d = v t, and t = d/v, if two are given, I can solve for the third (velocity is distance divided by time).(6 votes)

- is your distance from home is independent variable or dependent variable, please help!(3 votes)
- Independent because the distance from your home doesn't change(4 votes)

- In the name of this section it says it is inequalities, but this is not what I am doing in class, where do I find inequalities as in on a number line with the < and > symbols?(5 votes)
- Can a variable be another variable?(2 votes)
- A single quantity should be represented by only one variable, so you should not have two different variables used for the same thing. So if a question talks about finding Andy's age, you cannot use a and x both to represent the same thing. However, any variable can be named whatever you like so you can define a variable with any letter you want. You could also have two variables that are equal to each other such as y = x (linear parent function), but they are still two variables - one independent and one dependent, not just one variable which has a specific plot on a Cartesian plane.

If you are asking can you use other variables besides x and y to represent quantities, then yes you can define variables any way you want.(5 votes)

- I dont know how to do Algebra 1(2 votes)
- Does it have to be in a straight line?Also what does it mean if the line is not straight.(1 vote)
- it doesnt really matter if the line is straight or not(1 vote)

- what the difference between dependent and independent variable(3 votes)
- a dependant variable is a variable that depends on another number. 3x is a dependant variable becase it has a number that you are aplying it to. x is a independant varyable becase it isnt being aplied to a number.(1 vote)

- This video doesn't have anything to do with my question: https://www.khanacademy.org/mission/algebra/task/5594277661671424(3 votes)

## 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.