yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Dependent & independent variables | 6th grade | Khan Academy


2m read
·Nov 10, 2024

Let's say that you love to eat apples, and you are going to buy apples. So, A is the number of apples. But you also have a budget, so you have to care about cost. Let's say C is equal to the total cost, and let's say that the price of an apple is two dollars. So, two dollars per apple.

There are 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 going to be two dollars 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 makes it useful for different scenarios.

For example, on the left-hand side here, it's really easy to try out different A's and then think about how that will affect the cost. When it's written like this, we would call the variable that it's easy to try out different values the independent variable. 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.

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 I, and then you want to find out the number of apples.

More Articles

View All
Signs of sums on a number line | Integers: Addition and subtraction | 7th grade | Khan Academy
Let’s give ourselves some intuition and then some practice adding negative numbers. So, let’s start with negative 11 plus negative 3. So, first we can visualize what negative 11 looks like on a number line. Like this, I intentionally have not marked off …
The Loner's Path | Philosophy for Non-Conformists
The Loner’s Path | Philosophy for Non-conformists The path of nonconformity is alluring to those who don’t seek to follow the herd known as a society. Instead, they want to make unique individual choices in life, disregarding other people’s opinions and …
Last Season on MARS | MARS
Getting to Mars will be risky, dangerous, but it will be the greatest adventure ever in human history. Funny thing about Mars, it feels like Earth, but it is more hostile to life at any place on Earth. Ignition in the absence of gravity, lots of things ca…
Timur | 600 - 1450 Regional and interregional interactions | World History | Khan Academy
Where we left off in the last few videos, we saw the Empire of the Mongols fragment into the various Khanates. In the East, you have the Yuan Dynasty established by Kublai Khan, and then in the West, you have the Golden Horde, the Chagatai Khanate, and th…
Rental Income Podcast Interview: How I bought 3 properties by 22 years old
Inspiring interviews with today’s top landlords. This is the Rental Income Podcast. And now, Damle. My guest on the podcast today had incredible timing when he decided to start buying rental properties. He bought three properties at what, looking back on…
Is War Over? — A Paradox Explained
Violence and war. The insane brutality of ISIS continues, the Russians are invading Ukraine, and the Palestinians and Israelis continue to slug it out. Does that make you feel gloomy? Well, don’t. Because if you look at the numbers, war actually seems to …