Finite Mathematics, Chapter 1, 1.2, Section 1.2, Problem 24

Write a linear cost function for the situation: "For one-day rental, a car rental firm charges $\$44$ plus 28 cents per mile.

There is a fixed cost of $\$35$ even no items is produced. Thus, we have ordered pairs $(0,35)$ and $(8,395)$. Then, by usng two point
form, the cost function will be

$
\begin{equation}
\begin{aligned}
y - y_1 &= \frac{y_2 - y_1}{x_2 - x_1} (x - x_1)\\
\\
y - 35 &= \frac{395 - 35}{8 - 0} (x - 0)\\
\\
y - 35 &= 45x \\
\\
y &= 45x + 35
\end{aligned}
\end{equation}
$

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