Question

The table shows the amount of money Tyler earns for mowing lawns. Is the

relationship a proportional relationship? Complete the explanation.

Answer 1

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.

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.