Y-intercept

Rearrange your relationship into $y = mx + b$ and the intercept is $b$. The AP Physics 1 CED asks it directly in its graphing-skill guidance: what is the physical meaning of the y and x intercepts of the linearized graph? Its description of the Experimental Design and Analysis question says the slope or intercepts of the line may be used to determine a physical quantity.

Three cases where the intercept is the answer:

• $P = P_0 + \rho g h$ is printed on the AP Physics 1 sheet. Plot $P$ against $h$ and the intercept is $P_0$, the surface pressure, while the slope gives the fluid's density.
• $K_{\text{max}} = hf - \phi$ is printed on the AP Physics 2 sheet. Plot maximum kinetic energy against frequency and the slope is Planck's constant while the intercept is minus the work function.
• A velocity-time plot at constant acceleration has intercept $v_0$, the initial velocity.

Where the axis starts decides whether you can read it. An intercept lives at $x = 0$. If your horizontal scale begins at 0.20 because that is where the data begin, the leftmost point of the line is not the intercept, and quoting it as one is a real error rather than a rounding one. Either extend the axis back to zero or get the intercept from the line's equation.

An unexpected intercept is information. A plot that should pass through the origin and does not is usually reporting a systematic error, an instrument zero offset or a term the model left out.

Getting the plot straight first is linearization; the intercept is read off the best fit line.