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## anonymous one year ago find the direct relationship between x and y and determine whether the parametric equations determine y as a function of x x=(1/3)t-1 y^2=t^2

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1. IrishBoy123

get t in terms of x from this one: x=(1/3)t-1

2. anonymous

can you explain some more?

3. IrishBoy123

you have x=(1/3)t-1, ie an equation giving x in terms of t work it so that you have t in terms of x, ie t = .... use normal algebra

4. anonymous

is this correct so far? $t=((1/3)-1)/x$

5. whovianchick

y=3x+3, yes it's a function

6. IrishBoy123

isn't it $x=\frac{1}{3}t-1$??? all you have to do is move the t across to the RHS and the x across to the RHS, applying usual rules of maipulation

7. anonymous

oh so just t= $t=\frac{ 1 }{3 }x-1$

8. whovianchick

Well, you have to find out if y is a function of x. first of all, if x=1/3t-1, then 3x=t-3, and t=3x+3. Then if y^2=t^2, y=t, so y=3x+3. Which is a function. I don't know where you got t=1/3x-1. That's not right

9. IrishBoy123

no, i said "applying usual rules of manipulation". you can't just lift them out(!!) and switch them around an example if $$x = \frac{2}{3} t + 4$$ then $$x-4 = \frac{2}{3} t$$ $$\frac{2}{3}t = x-4$$ $$t = \frac{3}{2} x - 6$$

10. IrishBoy123

@whovianchick no, it is not a function but vinny has some work to do before we get there

11. whovianchick

Except that your math is wrong and you're forgetting y. Recheck your math. You can't just switch t and x, you have to solve for t. It's called 7th grade math. I'm in 11th grade math.

12. anonymous

sorry his wording confused me its t=3x-3 correct?

13. IrishBoy123

not quite

14. IrishBoy123

sign on the 3??

15. anonymous

positve

16. IrishBoy123

and when you have done that we are told that $$y^2 = t^2$$ so stuff your new equation into that

17. anonymous

ugh sorry im working on little sleep and silly mistakes are getting me'

18. whovianchick

|dw:1442362440473:dw|

19. IrishBoy123

thanks whovian:-)

20. IrishBoy123

keep going vinny, we are nearly done!

21. anonymous

y=3x=3

22. whovianchick

You're welcome. You had him working with the wrong equation, and I'm nitpicky like that

23. anonymous

ah they are squared gh

24. IrishBoy123

yes so just square them, DO NOT multiply/expand out the x side,...!

25. IrishBoy123

"You had him working with the wrong equation," when?

26. whovianchick

if y^2 = t^2, then y=t Replace y for t in the equation: y=3x+3, which is a function

27. anonymous

yeah thats what i did

28. anonymous

thanks guys

29. IrishBoy123

no vinny it is NOT a function

30. whovianchick

No prob. Sorry @IrishBoy123 earlier he said something like 1/3x-1 = t and I thought it was you

31. IrishBoy123

you will see why if we finish this properly but if you are really tired, go to bed

32. whovianchick

@IrishBoy123 UMMMMMMMMMMMM y=3x+3 IS a function

33. IrishBoy123

it is a function, thatis ture, but that is not what we have here

34. IrishBoy123

"thatis ture" that is true

35. whovianchick

|dw:1442362767682:dw|

36. whovianchick

That's the answer, I'm confused what you're saying

37. IrishBoy123

@vinny0515 are you done for the day?

38. IrishBoy123

this is what we have here |dw:1442362770822:dw|

39. whovianchick

No it's not, and both are functions

40. anonymous

so the answer for the quesrion is y=3x+3

41. IrishBoy123

no it is not

42. whovianchick

|dw:1442362943289:dw|

43. whovianchick

What is the answer, then? We've replaced y for t, and we're done. What the heck are you talking about?

44. whovianchick

y=3x+3 is the answer

45. anonymous

how do i answer it then

46. whovianchick

The way I told you to. y=3x+3, and yes it's a function

47. IrishBoy123

$$y^2=(3x+3)^2$$ is what you have if you want to simplify it you can say $$y= \color{red}\pm (3x+3)$$ but whatever you do, x maps to 2 y values it is not a function

48. anonymous

irsih boy is right

49. whovianchick

@IrishBoy123 I understand that. But it's saying as one line, is every solution a function. The answer is yes. Both of those equations are functions

50. IrishBoy123

it is not a function as you can get 2 y's for every x y = 3x+3 is a function y = -(3x+3) is a function this is both and is not a function |dw:1442363265605:dw|

51. IrishBoy123

and that's us done thank you both:p

52. anonymous

so i write the answer as y is not a function

53. whovianchick

Y is a function. I think you're forgetting the concept of a function, @IrishBoy123 , it's ok if there are multiple y's for every x. What you don't want is multiply x's for every y. THAT is the definition of a function, and even with your skewed logic, it's STILL a function. Stop confusing @vinny0515. YOU ARE WRONG

54. IrishBoy123

|dw:1442432889018:dw|

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