A student conducts an experiment with an optical bench to determine the focal length \(f\) of a thin converging lens. For several object distances \(d_o\), the student adjusts the position of a screen until a sharp, real image is formed at distance \(d_i\) on the opposite side of the lens, recording the data in the table.

Trial	Object Distance \(d_o\text{ (cm)}\)	Image Distance \(d_i\text{ (cm)}\)
1	15.0	30.0
2	20.0	20.0
3	30.0	15.0
4	50.0	12.5

The student plots \(\dfrac{1}{d_i}\) on the vertical axis as a function of \(\dfrac{1}{d_o}\) on the horizontal axis and fits a straight line of the form \(y = mx + b\) to the data. Which of the following correctly identifies the theoretical slope \(m\) of the line and the focal length \(f\) calculated from the vertical intercept \(b\)?