Break-even point

Definition

The break-even point is the value at which two linear functions intersect, indicating where a business neither profits nor loses. It is found by solving a system of linear equations.

5 Must Know Facts For Your Next Test

1. The break-even point occurs where the revenue and cost functions are equal.
2. It can be found by setting two linear equations equal to each other and solving for the variable.
3. Graphically, it is the point of intersection between the lines representing the equations.
4. In algebraic terms, if $y = mx + b$ and $y = nx + c$, solve for $x$ when $mx + b = nx + c$ to find the break-even point.
5. Breaking even means total revenue equals total costs, so there is no net gain or loss.

Review Questions

• How do you find the break-even point algebraically between two linear equations?
• What does it mean for a business to be at its break-even point?
• How can you determine the break-even point graphically?

Related terms

System of Linear Equations: A set of two or more linear equations involving the same variables.

Intersection Point: The coordinates at which two or more graphs meet, indicating solutions common to all equations involved.

Linear Function: A function that forms a straight line when graphed and can be expressed in the form $y = mx + b$.