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## Integrated math 1

### Course: Integrated math 1 > Unit 1

Lesson 2: Introduction to variables# What is a variable?

Variables in math are symbols, often letters, that represent different values in various situations. They help us understand and solve problems with changing values. For example, when calculating total earnings at a job with an hourly wage plus tips, a variable can represent the fluctuating tips, making it easier to determine total income. Created by Sal Khan.

## Want to join the conversation?

- Can you use a ! for a variable?(233 votes)
- Yes, you could but you might confuse it for a factorial.(8 votes)

- Where did they come up with the name variable?(107 votes)
- If something varies, it changes from time to time. A variable is so named because it is capable of changing, as opposed to a numerical value, which must remain constant. Let me explain.

x could be anything. 1, 5, 273, 50 trillion--anything. Thus, it can vary in its actual value. This potential variability gives it the name variable. In contrast, the number 5 cannot change its value. It always will be 5. If it held a value of something other than 5, it simply wouldn't be 5. In this way, its value is constant. Hence, it is named a constant.(99 votes)

- How do you graph functions?(74 votes)
- you need the table of points or the coordinates themselves. make the x and y axes on a piece of graph paper. You need an equation to plug in numbers for x and y variables too(29 votes)

- I know that x and y are the most common variables, but are you allowed to use other variables to? Like O?

Wondering,

Allie(37 votes)- Yes. At0:11, Sal uses "Tips" as the variable. At2:20, he uses T to represent time.(17 votes)

- So, the only reason we use lowercase letters for variables is to keep things simple? So that means we can still use words, but letters is easier, right?(20 votes)
- Letters are just shorter representations of objects. If we have 10 apples, it would be easier to write 10x, where x is being used to represent apples. It is much easier to use letters to represent variables rather than to write apples or whatever variable is being used.(8 votes)

- and what is tips

what is a variable

why do we use them

who created them(8 votes)- In this case, tips are the sum of money given to someone as a reward for a service. For exemple: give a tip for a good waiter.

Now, a variable can be anything, it depends of the statement. In Math, when you make a statement, then it can be false or true. But, if you put a variable in a statement, so the proposition can be false and true either for different values. Therefore, a variable works how a question. For exemple:

x + 2 = 4 . I have a statement and x is a variable because it can be any real number, but in truth it is a question: what numbers i can put in place the x and the results will be true? The answer how you know is 2. More one: y - 5 = 2 + x. Now, you have 2 variables and several responses. Thats why we use them: to work when we dont know the answer yet. In a function, for exemple, we have two variables: one is independent and other is dependent for the first one which means that when you change intentionally the independent then the dependent changes too. The speed is a exemple: if you have a constant speed, then the distance is the dependent variable and the time is the independent variable. How much more time pass, the distance you traveled increase in a same speed.

François Viète introduced at the end of 16th century the idea of representing known and unknown numbers by letters, nowadays called variables, and of computing with them as if they were numbers, in order to obtain, at the end, the result by a simple replacement. François Viète's convention was to use consonants for known values and vowels for unknowns.

In 1637, René Descartes "invented the convention of representing unknowns in equations by x, y, and z, and knowns by a, b, and c". Contrarily to Viète's convention, Descartes' is still commonly in use. I hope to have could help you. Good luck!(24 votes)

- Why are x and y the most common variables?(6 votes)
- René Descartes used letters from the end of the alphabet as variables, and letters from the beginning of the alphabet as constants. In particular, he used x for an independent variable and y for the dependent variable, the letters we use for the standard coordinates of the plane, along with z.(19 votes)

- Are variables hard and do they get harder in every grade you go in?(6 votes)
- Variables are hard at first. Variables themselves get easier to use the more you use them, as with any concept. Math classes tend to get harder because they will expect you to use more variables in different ways. Yet the harder the math you do, the easier it becomes to use variables, and other ideas, to solve problems in your life. For example, what score do you need on your next test to get an A? This is a question that is much easier to answer using variables than without them.(14 votes)

- are variables used in things that are not math? if yes, then what?(7 votes)
- Yes, the definition of a variable is anything that can change in a plan, for example weather can change so it can be counted as a variable in some cases.(8 votes)

- can variables be anything else but x?(4 votes)
- Yes, any letter could be used as a variable, though "x" is the most commonly used. There are some letters that people stay away from because they look too much like numbers, for example: lower case L look like one (1); the letter O looks like zero (0).(10 votes)

## Video transcript

Let's say that I'm
working in a restaurant, and I'm making $10 per hour. But on top of my hourly wage,
I also get tips each hour. So this entire expression,
you can view this as how much I might
make in a given hour. Now, you might also realize
that the number of tips or the amount of tips
I might make in an hour can change dramatically
from hour to hour. It can vary-- one hour it
might be lunchtime, get a lot of tips, people might
get some big-ticket items. The next hour, I might
not have any customers. And then my tips
might be really low. So the tips part
right over here, we consider that--
the entire word, we consider that
to be a variable. From scenario to
scenario, it can change. So for example, in one
scenario, maybe it's lunchtime. I'm getting really big tips. So tips is-- let's
say it's equal to $30. And so the total amount I
might make in that hour-- we can go back to this
expression right over here-- it's going to be 10 plus--
instead of writing tips here, I'll write 30 because that's
what my tips are in that hour. And so that is going
to be equal to 40. Let me do it in
that yellow color. It's going to be equal to $40. But let's say right after that,
the restaurant slows down. We're out of the lunch
hour for whatever reason. Maybe the restaurant next door
has a big sale or something. And so the next hour, my
tips go down dramatically. My tips go down to
$5 for that hour. Now I go back to
this expression. The total I make
is my hourly wage plus the $5 in tips,
which is equal to $15. As you see, this entire
expression-- the 10 plus tips-- it changed depending on what the
value of the variable tips is. Now, you won't see whole
words typically used in algebra as variables. We get lazy. And so instead, we tend to use
just easier-to-write symbols. And so in this context,
instead of writing tips, maybe we could have
just written 10 plus t, where t represents the tips
that we get in an hour. And so then we
would say, OK, what happens when t is equal to 30? Well, then, we have a situation. t is equal to 30. This evaluates to 10 plus
30, which would be 40. What would happen
if t is equal to 5? Well, then, this would
evaluate to 10 plus 5, which is equal to 15. Now, I want to be clear. We didn't even have to use t. We didn't even really
have to use a letter, although in traditional algebra,
you almost do use a letter. We could have written
it as 10 plus x, where x is your tips per hour.
x might not be as natural. It's not the first
letter in the word tips. Or you could have even
written 10 plus star, where you could
say star represents the number of tips in an hour. But it just might have not
made as much intuitive sense. But hopefully this
gives you a general idea of just what a variable is. All it is is a symbol that
represents varying values. And that's why we
call it a variable.