(a)
In order to find the equation, let's use the slope-intercept form of the linear equation:
![V=mt+b](https://img.qammunity.org/2023/formulas/mathematics/college/iihx1ysmzyu1ff0dmxh3oahca8l7s774b9.png)
Where m is the slope and b is the y-intercept.
Looking at the graph, the initial value for t = 0 is 11500, therefore the value of b is 11500.
To calculate the slope, we can use two points from the graph (let's use (0, 11500) and (1, 9500)) in the formula below:
![\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(11500-9500)/(0-1)=(2000)/(-1)=-2000 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/dwvqny0ehim4l5jcblqws4ue459g8mm3hc.png)
Therefore the equation is V = -2000t + 11500.