Question

Determine whether y varies directly with x. If so find the constant of variation k and write the equation.
x y
7 11
8 13
9 15
10 17

Answer 1

There seems to be a direct relationship, as an increase an x results in an increase in y, but we can check if:
y = kx

11 = 7k, k = 1.57
13 = 8k; k = 1.62
15 = 9k; k = 1.67
17 = 10k; k = 1.70

As we can see, the variation is not constant so this is not a simple direct relation.

Answer 2

Answer:

11 = 7k, k = 1.57

13 = 8k; k = 1.62

15 = 9k; k = 1.67

17 = 10k; k = 1.70

Step-by-step explanation:

There seems to be a direct relationship, as an increase an x results in an increase in y, but we can check if:

y = kx

11 = 7k, k = 1.57

13 = 8k; k = 1.62

15 = 9k; k = 1.67

17 = 10k; k = 1.70

Y does not have an direct variation with x.