What is the difference between a slope change and a translation

Translation describes movement of an object without change of size where as the change in slope describes the variation in steepness of an object. Step-by-step explanation: ... Slope is the ratio of vertical and horizontal changes between two points on a surface or line.

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50