Question

x: 4, 7, 10, 13
y: 6.4, 11.2, 16, 20.8
Determine whether y varies directly with x. If so, find the constant variation k and write the equation.

Answer 1

To determine if y varies directly with x, we need to check if the ratios of corresponding elements in the two sets are the same for all elements. Let's calculate the ratios:

x: 4, 7, 10, 13
y: 6.4, 11.2, 16, 20.8

The ratio for the first pair is:
6.4/4 = 1.6

The ratio for the second pair is:
11.2/7 ≈ 1.6

The ratio for the third pair is:
16/10 = 1.6

The ratio for the fourth pair is:
20.8/13 ≈ 1.6

Since the ratios are the same for all elements, we can conclude that y varies directly with x. The constant of variation, k, is the common ratio. In this case, k is approximately 1.6.

The equation of variation is y = kx. Substituting the value of k, the equation becomes:
y = 1.6x