Question

Maya accepted a new job at a company with a contract guaranteeing annual raises. Let SS represent Maya's salary after working for nn years at the company. The table below has select values showing the linear relationship between nn and S.S. Determine Maya's salary when hired.

Answer 1

well, we know that the relationship of "n" and "s" is linear, so hmmm let's get their equation first.

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

`(\stackrel{x_1}{7}~,~\stackrel{y_1}{68000})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{76000}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{76000}-\stackrel{y1}{68000}}}{\underset{run} {\underset{x_2}{9}-\underset{x_1}{7}}} \implies \cfrac{ 8000 }{ 2 } \implies 4000`

`\begin{array} \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}{68000}=\stackrel{m}{ 4000}(x-\stackrel{x_1}{7}) \\\\\\ ~\hfill {\Large \begin{array}{llll} s-68000=4000(n-7) \end{array}} ~\hfill`

now, when she was hired, well that was when there were no years, namely at year 0, so we can say that's when n = 0

`s-68000=4000(n-7)\implies s-68000=4000(\stackrel{n}{0}-7) \\\\\\ s-68000=4000(-7)\implies s-68000=-28000 \\\\\\ s=-28000+68000\implies {\Large \begin{array}{llll} s=40000 \end{array}}`