Derivative of a Linear Function

Let f be a function whose graph is a straight line of the form y = mx + c
∴ f(x) = mx+c   when x = 0 f(0) = c so c represents the cut on the y-axis
also if x ≠ 0 the slope of the line joining the points (0,c) and (x,y) is given by

y − c Let this slope = m ∴ m = ——  ⇒   y = mx +c
x  
From the definition of the derivative if f(x) = mx + c

f(x+h) − f(x) f '(x) = ————— where h ≠ 0
h ∴ f '(x) = m ∀x for a linear function