Answer:
The constant of variation 'k' is NOT constant.
Therefore, we conclude that Taylor did not charge a constant rate. The rates are not equal because his rate changed.
Step-by-step explanation:
Given the table
Number of Lawns 1 2 3 4
Amount Earned ($) 16 32 54 72
We know that when y varies directly with x, we get the equation
y ∝ x
y = kx
k = y/x
where 'k' is called the constant of proportionality.
In our case, the 'Amount earned ($) ' is represented by 'y', and the 'Number of Lawns' is represented by 'x'.
Let us check the constant of proportionality using the equation
k = y/x
k = 16/1 = 16
k = 32/2 = 16
k = 54/3 = 18
k = 72/4 = 18
It is clear that that the constant of variation 'k' is NOT constant.
Therefore, we conclude that Taylor did not charge a constant rate. The rates are not equal because his rate changed.
