Break-even point

Definition

The break-even point is the point at which total revenue equals total costs, resulting in neither profit nor loss. In algebraic terms, it is found by solving a system of linear equations where the cost and revenue functions intersect.

5 Must Know Facts For Your Next Test

1. The break-even point can be represented graphically as the intersection of the cost and revenue lines.
2. To find the break-even point algebraically, set the cost function equal to the revenue function and solve for the variable.
3. In a linear system, both cost and revenue are typically represented as linear equations in two variables (e.g., $C(x) = m_1x + b_1$ and $R(x) = m_2x + b_2$).
4. The coordinates of the break-even point give both the quantity produced/sold (x-value) and the corresponding cost/revenue (y-value).
5. Understanding how to calculate and interpret the break-even point is crucial for making informed business decisions.

Review Questions

• How do you find the break-even point using a system of linear equations?
• What does it mean graphically when you find a break-even point?
• If given two linear equations representing cost and revenue, how would you solve for their intersection?

Related terms

Linear Equation: An equation that makes a straight line when graphed. Standard form is $Ax + By = C$.

System of Equations: A set of two or more equations with the same variables. Solutions to systems are points where all equations intersect.

Inequality: A mathematical statement that compares expressions using inequality signs like $<$, $\leq$, $>$, $\geq$. Solutions are often represented on number lines or coordinate planes.