Aramp with a constant incline is made to connect a driveway to a front door. at a point 4 feet from the driveway, the height of the ramp is 12 inches. at a point 6 feet from the driveway, the height of the ramp is 18 inches. what is the rate of change of the ramp’s incline?

At first glance we can think of this as a question just asking for slope of the line like in the diagram. However..

It is not the only way. We could make an equation for slope and find the derivative, but this isnt needed.

12/4 =  3  = 18/6

Another way is to make a small triangle inside the shorter one.

height = (18 - 12)
width = (6-2)

h = 6, w = 2

slope = rise/run = h/w  = 6/2 = "3"

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