After 2 years, a boat has a value of $36000. After 8 years, its value is $9000. Assuming a linear function, write an equation in the form v(t)=mt+b that shows the value of the boat, v(t), after t years of depreciation.

Answer:[tex]v(t)=-4500 t + 45000[tex]Step-by-step explanation:We are trying to graph a line on the two dimensional plane that represents the value of the boat in the vertical axis, and the years that have elapsed since its purchase in the horizontal axis.We have information to furnish two points on that plane with coordinates that show (number of years, value at that time). These are:(2, 36000) for the value of the boat 2 years after purchase : $36000and another one:(8, 9000) for the value of the boat 8 years after purchase : $9000We use them to find the slope of the line that joins them with the familiar formula:slope = \frac{y2-y1}{x2-x1}  = \frac{9000-36000}{8-2} = \frac{-27000}{6} = -4500[/tex][/tex]Therefore our line so far can be written as: [tex]Value(t) = -4500 t + b[/tex]in order to find the vertical intercept, we evaluate the line at one of the given points, for example at (2, 36000):[tex]36000 = -4500 (2) + b[/tex][tex]36000 = -9000 + b[/tex]therefore, b = 36000 + 9000 = 45000The line is : [tex]Value (t) = - 4500 t + 45000[/tex]