How Is the Moment of Inertia Constant Determined Experimentally?

[stalebrownie]

Homework Statement

For a little background, this lab was on energy of a rolling object. We rolled a hollow cylinder from the top of a ramp on a table and onto the floor. We are trying to experimentally derive the constant (k) found in the equation for moment of inertia.

Variables: h = height from top of ramp to table, H = height from table to floor, x = distance ball travels from end of ramp to its landing on floor

Make a graph of x^2 vs h. Add a trendline. Calculate k from the slope of the trendline as it corresponds to x^2 = (4Hh)/(k+1)

My trendline equation is x^2 = 1.98h - .086

Homework Equations

I = kmr^2
x^2 = (4Hh)/(k+1)
We know theoretically that k=1 for a hollow cylinder

The Attempt at a Solution

At first I thought the slope was k but that doesn't make sense because my expected k is 1.
I could just calculate k given my experimental measurements, but that's not what they're asking. I'm trying to relate the given equation to mx+b form but I'm drawing a blank. I don't know how to start.

Thanks!

 

[rock.freak667]

You have x² = (4Hh)/(k+1) ⇒ x² = (4H/(k+1)) h

this is in the form Y=MX+C, Y=x² and X=h. What is M?