Is the letter y special in mathematics? Find out the answer to this question in this lesson. Also discover the various applications of this variable and how you will use it to solve problems.

What Is the y Variable?

A variable is anything used to identify an unknown number in math. It could be a letter, a symbol, or anything else you can write or draw. It could be an empty box that you have to fill up with an answer. Here are some examples.

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Examples of variables
y variable 1

While a variable can be anything you can think of, in math, it is usually letters. The letter y is commonly used as a variable in math. It is probably one of the first variables you will come across. It is usually used when referring to equations that you graph. It also is used to refer to functions.

Does it have to be a letter y? No, any letter can take its place. But because the use of the letter y is so common, it is generally the preferred letter to use. Even if you see the letter y everywhere, keep in mind that it could be any letter. Get comfortable with the idea that another letter can have the same meaning as the letter y.

The y Variable in Graphing

You are most likely to come across the y variable when asked to graph. The most common formula for graphing is called the slope-intercept form.

y variable

This formula makes it easy to graph on the Cartesian coordinate plane. The letter m stands for slope and the letter b stands for the y-intercept. The y-intercept is the point on the y-axis where the line crosses. You’ll see equations like y=3x+2 and y=-4x-5. An equation written in slope-intercept form will always look like that.

Graphing the slope-intercept form is a two-step procedure. First you would locate the y-intercept b on your Cartesian coordinate and place a point on it. Then you would find your slope and go from your point to the next following the slope. Slope is rise over run. So, if your slope is 2, then you would go up 2 and to the right 1 from your first point.

Graphing an equation in slope intercept form.
y variable

The y Variable in Functions

Another use of the y variable that you will across is when it is used to denote a function.

The y variable denoting a function
y variable

When used to denote a function, the y can be written by itself or in the form of y(x) to make it known that the y function depends on the x variable. You can have the y variable dependent on any other letter too.

The y variable dependent on other variables
y variable

If you are given a function and asked to evaluate it at a certain point. you might see the problem written as y(3) if asked to evaluate the function at 3. To evaluate it, you would plug in the 3 for any variables you see in the function and perform the operations to get your answer.

Lesson Summary

The y variable does the same job as any other variable, which is that of identifying unknown values. They are placed wherever the unknown value would be. Variables can be any letter. The y variable is most often seen in graphing equations and in functions.

Learning Outcomes

When you are done with this lesson, you will have the ability to:

  • Describe what the y variable is
  • Explain the y variable in graphing
  • Discuss the use of the y variable in functions