Linearization

The AP Physics 1 CED states it plainly: in the Experimental Design and Analysis question on the exam, students "will also be asked to linearize and analyze data". That is one of the four free-response questions, and the free-response section carries 50 percent of the exam.

The method is always the same four steps.

1. Write the relationship you expect, then rearrange it into the shape $y = mx + b$.
2. Decide which combination of measured quantities plays the part of $y$ and which plays $x$.
3. Plot those, and draw a best fit line through all the points rather than through the first and last.
4. Take the slope, and solve the expression it equals for the constant you want.

A simple pendulum obeys $T = 2\pi\sqrt{\ell/g}$, which is a curve. Square it: $T^2 = (4\pi^2/g)\,\ell$. Plot $T^2$ against $\ell$ and the slope is $4\pi^2/g$, so $g = 4\pi^2/\text{slope}$.

Pressure with depth obeys $P = P_0 + \rho g h$, which is already linear. Plot $P$ against $h$ and the slope is $\rho g$, giving the fluid's density; the intercept is the surface pressure. That is the CED's own model answer for its fluids laboratory question.

The slope is a combination of constants with units, never the constant itself. Say what it equals before you divide.