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

As equation for y varies directly with x with constant of variation k is y = kx .

(1 )Equation becomes 11 = 7k and constant of variation is 1.57 .

(2)Equation becomes 13 = 8k and constant of variation is 1.625 .

(3)Equation becomes 15 = 9k and constant of variation is 1.67 .

(4)Equation becomes 17 = 10k and constant of variation is 1.7 .

Explanation:

As given

y varies directly with x.

`y \propto x`

y = kx

Where k is the constant of variation .

As given

x = 7 , y = 11

Equation becomes

11 = 7k

`k = (11)/(7)`

k = 1.57 (Approx)

Thus equation becomes 11 = 7k and constant of variation is 1.57 .

As given

x = 8 , y = 13

Equation becomes

13 = 8k

`k = (13)/(8)`

k = 1.625

Thus equation becomes 13 = 8k and constant of variation is 1.625 .

As given

x = 9 , y = 15

Equation becomes

15 = 9k

`k = (15)/(9)`

k = 1.67 (Approx)

Thus equation becomes 15 = 9k and constant of variation is 1.67 .

As given

x = 10 , y = 17

Equation becomes

17 = 10k

`k = (17)/(10)`

k = 1.7 (Approx)

Thus equation becomes 17 = 10k and constant of variation is 1.7 .

Answer 2

The correct answer is that y does not vary directly with x.

Explanation:
If y varies directly with x, this means that it would fit the equation y=kx for every point in the set.

For the first point, we would have 11=7k; this would mean that k=11//7.
For the second point, we would have 13=8k; this would mean that k=13/8.

Checking using proportions shows us that 11/7 does not equal 13/8:
cross multiply, and you have 11*8=7*13, or 88=91.

This is not true, so k is not a constant, and y does not vary directly with x.