Break-even point-Definition and example

A break-even point is the point at which the income of a business is equal to the expenses of the business. The graph below shows the break-even point with a black dot for one business.

Break-even point

Notice that the values of y on the green line represent dollars received as income and the values of y on the red line represent dollars spent on expenses. Therefore, y is used to represent both income and expenses.


To run a business, you need to spend 2 dollars for each item sold plus 100 dollars in extra fees. The selling price of each item is 3 dollars. What is the break-even point? 

Let x be the number of items sold and let y be the amount of dollars of income and expenses.

Income = selling price times number of items sold 

y = 3x

Expenses = cost for the number of items sold plus cost of extra fees

y  = 2x + 100

The break-even point occurs when the income of the business is equal to the expenses of the business.

3x = 2x + 100

3x - 2x = 2x - 2x + 100

x = 100

The break-even point for this business occurs when you sell 100 items 

y = 3x = 3(100) = 300

y = 2x + 100 = 2(100) + 100 = 200 + 100 = 300

Break-even point

Recent math words

  1. Straight Angle - Definition and Examples

    Dec 01, 21 10:55 AM

    What is a straight angle? A straight angle is an angle that has a measure of ...

    Read More

  2. Unlike Fractions - Definition and Examples

    Dec 01, 21 04:38 AM

    What are unlike fractions? Definition, explanation, and examples

    Read More

Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.
Share this page: