What is the purpose of finding the slope of a line?

A synonym for the slope of a line is the rate of change. However, one purpose for the slope of the line is the determine whether the linear relationship has a positive correlation or a negative correlation. Based off of this, your answer most likely is D.

adding a(n) to an electric circuit would increase the magnetic field around a wire;

b. solenoid

a solenoid is a type of electromagnet whose purpose is to generate a controlled magnetic field.

if the purpose of the solenoid is instead to impede changes in the electric current, a solenoid can be more specifically classified as an inductor rather than an electromagnet.