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Determining if an Equation Defines a Function

Example

Example: Determining if the Equation $2x + y = 7$ Defines a Function

Consider the equation $2x + y = 7$ . To determine if it defines a function with $x$ as the independent variable, isolate $y$ . Solving for $y$ yields $y = -2x + 7$ . For any value substituted for $x$ , multiplying it by $-2$ and adding $7$ produces exactly one corresponding value for $y$ . For instance, if $x = 3$ , then $y = -2(3) + 7$ , which evaluates to $1$ . Because each value of $x$ corresponds to only one value of $y$ , the equation $2x + y = 7$ defines a function.

Updated 2026-05-06

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OpenStax Intermediate Algebra

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