Models which are linear in the variables have constant slopes. This slope is the same at all values of X i where we might want to compute a slope.
Straight lines have constant slope.
Its slope with respect to Z i is constant and equal to b 3 . Taking the derivative of a sum of terms yields the sum of the derivatives of each term. Since X i appears only in the second term in the sum, and nowhere else, only the derivative of this second term with respect to X i is relevant to the derivative of the whole expression with respect to X i . In general, the derivative of x 2 with respect to x is 2x. It changes according to the value of X i at which it is being assessed.