## sapphers 2 years ago 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

1. jim_thompson5910

If y varied directly with x, then y = k*x for some fixed constant number k

2. jim_thompson5910

Using this info, what is k?

3. sapphers

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

4. jim_thompson5910

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

5. jim_thompson5910

y = k*x 11 = k*7 Now solve for k

6. sapphers

Oh that makes more sense! Okay (:

7. jim_thompson5910

So what is k when you solve that last equation?

8. sapphers

Could I do 11/7? K=1.57

9. jim_thompson5910

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

10. sapphers

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

11. jim_thompson5910

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.

12. sapphers

Oh alright

13. jim_thompson5910

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

14. tcarroll010

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.