College Algebra, Chapter 3, 3.2, Section 3.2, Problem 58

Determine whether the equation $3x + 7y = 21$ defines $y$ as a function of $x$.

Solving for $y$ in terms of $x$ gives


$
\begin{equation}
\begin{aligned}

3x + 7y =& 21
&& \text{Subtract } 3x
\\
\\
7y =& 21 - 3x
&& \text{Divide both sides by } 7
\\
\\
y =& \frac{21 - 3x}{7}
&& \text{Simplify}
\\
\\
y =& 3 - \frac{3}{7} x
&& \text{Answer}

\end{aligned}
\end{equation}
$


The last equation is a rule that gives one value of $y$ for each value of $x$, so it defines $y$ as a function of $x$. We can write the function as $\displaystyle f(x) = 3 - \frac{3}{7} x$

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