Question

In 2011​, airlines earned ​$33.7 billion in revenue from ​add-on fees. In ​2012, they earned ​$48.7 billion from​ add-on fees. Determine a linear​ model, R(x) for the airline revenue earned from​ add-on fees x years after 2006.

Answer 1

to get the equation of any straight line, we simply need two points off of it, let's use those two provided in the picture below.

`(\stackrel{x_1}{5}~,~\stackrel{y_1}{33.7})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{48.7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{48.7}-\stackrel{y1}{33.7}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{5}}} \implies \cfrac{15}{1}\implies 15`

`\begin{array}c \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{33.7}=\stackrel{m}{15}(x-\stackrel{x_1}{5}) \\\\\\ y-33.7=15x-75\implies {\Large \begin{array}{llll} y=15x-41.3=R(x) \end{array}}`