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# )