Kinematics/calculating a line from a curve?

[fruitbowl]

Homework Statement

"If only the variables D and t are used, what quantities should the student graph in order to produce a linear relationship between the two quantities?"

The data:
distances (m): .1, .5, 1, 1.7, 2
Time(s): .14, .32, .46, .59, .63

Basically, a student is dropping a ball from several points and recording how long the fall took from each point. They're trying to experimentally determine g. So the data yields a curve. The full problem is here, it's the first one after the reference sheet: http://apcentral.collegeboard.com/apc/public/repository/_ap06_frq_physicsb_fo_51783.pdf

Homework Equations

n/a

The Attempt at a Solution

I'm not exactly sure what the question is asking. Since the data gives a curve, but I need a line, The "quantities" they want are the end points of the line segment that approaches all the points in the curve the most, right? How do I get that?

I tried graphically, this is the best I could get:

But there's got to be a math way to do it. Please help...

 

[rock.freak667]

Well you know that

D=ut+1/2at² which simplifies to D=1/2gt²

You can plot appropriately to get a straight line.

 

[fruitbowl]

I'm sorry to seem so dense but- what do you mean? what do I plot? D=1/2gt^{^2} is still a curve...

 

[rock.freak667]

I'm sorry to seem so dense but- what do you mean? what do I plot? D=1/2gt^{^2} is still a curve...

If you make the equation into the form Y=MX+C and plot Y vs. X you will get a straight line. Put Y=D, what should X be to get a straight line?