Convert the equation for the line from point-slope form to function notation. For example, y = 3/5 * x +15 becomes f (x) = 3/5 * x +15.
Differentiate the first term of the equation. Using the general power rule for derivatives, the derivative of x^n = n * x^(n-1), the first term simplifies to 3/5 instead of 3/5 * x resulting in f (x) = 3/5 + 15.
Differentiate the second term of the equation. Using the constant property" of derivatives, the derivative of the constant always equals 0. Therefore, the second term of the equation is set to zero and removed from the equation, leaving f (x) = 3/5.
Rewrite the resulting terms in function notation. Specifically, f (x) = 3/5 becomes f ' (x) = 3/5. The apostrophe after the "f" signifies that this function is the first derivative of f (x) and is spoken: "f prime of x," giving the slope of the line as 3/5.