College Algebra, Chapter 2, 2.4, Section 2.4, Problem 76

According to the manager of a furniture factory, it costs $\$2200$ to manufacture 100 chairs in one day and $\$ 4800$ to produce 300 chairs in one day.

a.) Assume that the relationships are linear, find an equation that expresses this relationship. Then graph the equation.

b.) What is the slope of the line in part (a) and what does it represent?

c.) What is the $y$-intercept of this line, and what does it represent?

a.) By using two point form, the slope of the points $(100, 2200)$ and $(300, 4800)$ is..

$\displaystyle m = \frac{4800 - 2200}{300 - 100} = \frac{2600}{200} = 13$

By using two point form,


$
\begin{equation}
\begin{aligned}

y =& mx + b
&&
\\
\\
y =& 13 x + b
&& \text{Substitute the value of the slope}
\\
\\
2200 =& 13(100) + b
&& \text{Solve for } b
\\
\\
b =& 900

\end{aligned}
\end{equation}
$


Thus, the equation is..

$y = 13x + 900$







b.) The slope of the line is 13, it represents the cost per chair produced.

c.) The $y$-intercept is 900, it represents the cost outside production, regardless of the number of chairs produced. Maybe for maintenance cost or rental cost.