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

Can someone please help me and explain

Answer 1

If y varied directly with x, then

y = k*x

for some fixed constant number k

Answer 2

Using this info, what is k?

Answer 3

I don't know. How do you find it? I really don't understand this.

Answer 4

The idea is that if you multiply each x term by some fixed number (the same fixed number) and you get the corresponding y value, then this is a direct variation

Here's a simple example

x y
------
1 2
2 4
3 6

If we multiply each x by 2 we'll get the correct corresponding y value, so this is a direct variation

Answer 5

y = k*x

11 = k*7

Now solve for k

Answer 6

Oh that makes more sense!
Okay (:

Answer 7

So what is k when you solve that last equation?

Answer 8

Could I do 11/7?
K=1.57

Answer 9

So if this was a direct variation, then we should be able to multiply each x by 11/7 or roughly 1.57 to get the corresponding y value

But...

When x = 8, k*x is (11/7)*8 = 88/7 which is roughly 12.57 and NOT 13

So this can't be a direct variation

Answer 10

Since it's not, what am I supposed to do? Just leave it like that or..

Answer 11

Just say it's not a direct variation. If it was a direct variation, then you would proceed to find k or show/say what k is.

Answer 12

Oh alright

Answer 13

since it says "If so find the constant of variation k and write the equation"

Answer 14

jim is right and he proved that there is no direct constant for proportionality between y and x, so you don't have to do anything else but state that. There IS an equation (actually lots of them) that you could write to show a relationship between y and x, but you are not required to find one since none will exhibit a directly proportional relationship between y and x.