y = 4 + 2x What does the slope of this function represent?

Question

The function below models the correlation between the number of hours a plant is kept in sunlight (x) and the height (y), in mm, to which it grows:

y = 4 + 2x

What does the slope of this function represent?

Answer 1

The slope of this function, which equals 2, represents the rate of change in the height of the plant with respect to the change in sunlight. In other words, for every one unit of change in sunlight, height increases by two units. We will see this if we plug in values for x

x= 1, y = 6

x = 2, y = 8

x = 3, y = 10

x = 4, y = 12

Answer 2

The slope is the rate of increase in y with respect to x, which is the rise in y divided by the advance in x.  In this particular problem, a slope of 2 means that the plant grows by 2 mm (y) for every hour that it is kept in sunlight (x).  So its growth rate is 2 mm per hour of sunlight, and it is constant while under sunlight.  That is the meaning of the slope in this problem.