Considering the function (linear): #y=mx+b# where m and b are real numbers, the derivative, #y'#, of this function (with respect to x) is:
#y'=m#
This function, #y=mx+b#, represents, graphically, a straight line and the number #m# represents the SLOPE of the line (or if you want the inclination of the line).
As you can see deriving the linear function #y=mx+b# gives you #m#, the slope of the line which is a quite rearcable result, widely used in Calculus!
As an example you can consider the function:
#y=4x+5#
you can derive each factor:
derivative of #4x# is #4#
derivative of #5# is #0#
and then add them together to get:
#y'=4+0=4#
(Remember that the derivative of a constant, #k#, is zero, the derivative of #k*x^n# is #knx^(n-1)# and that #x^0=1# )
