Question

Find the slope passing through the points, write a linear function that expresses the value of this computer and what is the value of the computer after 5 years?

Answer 1

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

`(\stackrel{x_1}{2}~,~\stackrel{y_1}{880})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{440}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{440}-\stackrel{y1}{880}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ -440 }{ 2 } \implies \boxed{-220}`

`\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}{880}=\stackrel{m}{-220}(x-\stackrel{x_1}{2}) \\\\\\ y -880 = -220 x +440 \implies y = -220 x +1320\implies \boxed{v(t)= -220 x +1320} \\\\[-0.35em] ~\dotfill\\\\ \textit{how about after 5 years? when x = 5?} \\\\\\ v(5)=-220(5)+1320\implies \boxed{v(5)=220}`