If we treat the data as a set of points ordered pairs #(t, V)#, then we are given the data as #(0, 1700), (4, 1540), (8, 1380)#. The first thing we need find a linear function is its slope #m#.
Given two points #(x_1, y_1)# and #(x_2, y_2)# on the graph #y = f(x)# of a linear equation, we can find the slope as the ratio of the change in #y# to the change in #x#.
#m = (triangley)/(trianglex) = (y_2-y_1)/(x_2-x_1)#
Picking the first two points from the data set, we get the slope of our desired function as
#m = (1540-1700)/(4-0) = -160/4 = -40#
Now that we have the slope, we can choose a point and use the point-slope form of a linear equation, #y-y_1=m(x-x_1)#, to find the equation of the graph #y=f(x)#.
Taking the first point #(0, 1700)# and the slope #-40#, we get
#y-1700 = -40(x-0)#
#=> y-1700 = -40x#
#=> y = -40x+1700#
Thus, our linear function is #f(x) = -40x+1700#
