The table shows the linear relationship between the average height in feet of trees on a tree farm and the number of years since the trees were planted.%0D%0A%0D%0ANumber of Years Since the Trees Were Planted%0D%0AAverage Height (ft)%0D%0A1%0D%0A12%0D%0A4%0D%0A39%0D%0A9%0D%0A84%0D%0A16%0D%0A147%0D%0AWhat is the rate of change of the average height in feet of the trees on the farm with respect to the number of years since the trees were planted?

Question

The table shows the linear relationship between the average height in feet of trees on a tree farm and the number of years since the trees were planted.%0D%0A%0D%0ANumber of Years Since the Trees Were Planted%0D%0AAverage Height (ft)%0D%0A1%0D%0A12%0D%0A4%0D%0A39%0D%0A9%0D%0A84%0D%0A16%0D%0A147%0D%0AWhat is the rate of change of the average height in feet of the trees on the farm with respect to the number of years since the trees were planted?

Answer 1

To find the rate of change of the average height in feet of the trees on the farm with respect to the number of years since the trees were planted, we need to determine the slope of the linear relationship.

We can use the formula for the slope of a line: slope = (change in y) / (change in x).

Let's choose the first and last points from the table to calculate the slope.

First point: (1, 12)
Last point: (16, 147)

change in y = 147 - 12 = 135
change in x = 16 - 1 = 15

slope = 135 / 15 = 9

Therefore, the rate of change of the average height in feet of the trees on the farm with respect to the number of years since the trees were planted is 9 feet per year.