1. Piecewise linear graph of the data.

In the proposed solution, we have created a list, a graphic for the enlarged points, and a second graphic for the connecting line segments. Finally, we show the graphs on the same set of axes.

Input := 

thePoints={{0, 0}, {.025, .8},{.05, 2}, {.075, 3},
    {.1, 3},{.125, 7.5}, {.15, 9}, {.175, 3}, {.2, 0}};

Input := 

s=ListPlot[thePoints,
    PlotStyle->PointSize[1/40],
	DisplayFunction->Identity,
	AxesLabel -> {TIME, POWER},
	PlotLabel -> BATTING POWER];

Input := 

t=ListPlot[thePoints,
    PlotJoined->True,
    DisplayFunction->Identity];

Input := 

Show[{s,t}, DisplayFunction->$DisplayFunction]

Output =

-Graphics-