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## 6th grade (Illustrative Mathematics)

### Course: 6th grade (Illustrative Mathematics) > Unit 6

Lesson 16: Lesson 16: Two related quantities, part 1# Dependent & independent variables

We introduce independent and dependent variables: how to identify the independent/dependent variable in a given setting, and how we write equations with the dependent variable by itself. Created by Sal Khan.

## Want to join the conversation?

- This is confusing(13 votes)
- It depends whether a variable is dependent or independent. In the video, he presents two scenarios:

scenario 1: you want to buy a certain number of apples

scenario 2: you have a limited budget.

In the first scenario, the number of apples (a) is the independent variable, but in the second one it's the total cost (c) sincedecide how many apples or how much your budget is, the**you***dependent*variable*depends*on**your decision**of the independent variable.

Here's another analogy, a dependent variable is like a passenger in a car, and an independent variable is like the driver. The driver (the independent variable) determines the car's direction and speed, while the passenger (the dependent variable) goes along for the ride. In the same way, the value of the dependent variable depends on the value of the independent variable.(7 votes)

- how did get the apples(5 votes)
- Can someone tell me simply what an independent and dependent variables are and how they are different?(2 votes)
- independent variables are called by other names such as input, domain, etc. and dependent variables are called by output, range, etc. So you have to start with something to put into an equation (independent) to be able to calculate something (output). When we are thinking more abstract, we generally use x for input and y for output.

In Math and Science, you get equations that could shift inputs and outputs as needed. If you have A=bh, you could be given b and h as inputs to calculate A, or we could be given A and h to find b, so we would have to use b=A/h. Same thing would happen with h. We will often see the dependent variable isolated on one side by itself, but not always.(7 votes)

- are you a person(4 votes)
- why did we have to bring the alphabet into math?!?!(4 votes)
- Apples are now 2$?(4 votes)
- wait, if the independent and dependent variables are interchangeable, how do we know which to label as which (idk if that made sense)?(4 votes)
- The dependent and independent variables change according to how you make the equation. Generally, dependent variables stay alone on one side of the equation, while the independent ones are in an operation(sum, subtraction, multiplication, division and so on).

Using the video example:

c = 2a --> c is dependent and a is independent(because it is multiplied by 2)

a = c/2 --> a is dependent and c is independent(because it is divided by 2)(0 votes)

- dang inflation really smacked us civilians(3 votes)
- i need help pls(3 votes)

## Video transcript

- [Teacher] Let's say that
you love to eat apples, and you are going to buy a apples, so a is the number of apples, number of apples, but you also have a budget, so you have to care about costs, so let's say C is equal to the total cost, and let's say that the
price of an apple is $2, so $2 per apple. There's several ways that we
can express the relationship between the total cost
and the number of apples. One way is if we solve for the total cost, and we say, okay, the total
cost is gonna be $2 per apple times the number of apples, so it's going to be 2a. Another way that we could rewrite this if we were to divide both
sides of this by two, we would get that the number of apples is equal to cost over two. These are equivalent
expressions I should say these are equivalent equations, but the way they've been written, make it useful for different scenarios. For example, on the left-hand side here, it's really easy to try out different As and then think about how
that will affect the cost, and so when it's written like this, we would call the variable that it's easy to try
out different values, we would call that the
independent variable, independent variable, and then the one that we
are essentially solving for that we then spit out a value after we compute using
the independent variable, you call that the dependent variable. You could view it as, look in this situation, the cost is dependent
on the number of apples you choose to eat. Now, when we wrote it over here, this looks a little bit different. Now the number of apples is solved for, and we compute how many
apples based on the cost, so this would be a scenario
where you have a budget and you tell me what the budget is and I could tell you the number of apples. So in this situation, C is the independent variable, and since we have solved for a, a is the dependent variable. This is useful if I give
you a number of apples and you want to know the total cost, and this is useful if
you have a certain cost and then you want to find
out the number of apples.