## anonymous one year ago 4. If x = 20 when y = -4, find y when x = 10.

1. anonymous

Is this a linear equation, @dianolove?

2. anonymous

Wait, couldn't you do: \begin{align} y&=kx\\ -4&=k\times20\\ k&=\dfrac{-1}{5} \end{align}

3. anonymous

this is the question it asked me Suppose that x and y vary inversely. Write a function that models each inverse variation. Then use the equation to solve the problem.

4. anonymous

Let's solve your equation step-by-step. 20x−4x=10 Step 1: Simplify both sides of the equation. 20x−4x=10 Simplify: (Show steps) 16x=10 Step 2: Divide both sides by 16. 16x16=1016 x=58 Answer: x=58

5. anonymous

do you under stand

6. anonymous

20x−4y=10

7. phi

*** x and y vary inversely*** means you can write the formula $y = \frac{k}{x}$

8. anonymous

it is a inverse variation and your solving for y not x

9. phi

that formula is useful if we know what "k" is. to find k, we use the info If x = 20 when y = -4, find y when x = 10.

10. phi

in other words, replace x with 20 and y with -4 into the formula $-4= \frac{k}{20}$ and "solve for k" by multiplying both sides by 20

11. phi

can you find what k is ?

12. anonymous

k is -80

13. phi

yes, so now you know the formula (for this problem) is $y = \frac{-80}{x}$ find y when x = 10. to find y, replace x with 10 in the formula and simplify

14. anonymous

y=-8

15. phi

yes

16. anonymous

thanks phi will you keep helping me with these i got another one

17. phi

ok

18. anonymous

If x = 5 when , find y when x = 10.

19. phi

missing some info

20. anonymous

5. If x = 5 when y=-1 third , find y when x = 10.

21. phi

do you mean if x=5 when y = $$- \frac{1}{3}$$ ?

22. anonymous

sorry mines will not do that but yes

23. anonymous

is k -30

24. phi

you could type it as y= -1/3 $y = \frac{k}{x} \\ - \frac{1}{3} = \frac{k}{5}$ to find k, multiply both sides by 5 $- \frac{1}{3} \cdot 5 = \frac{k}{5}\cdot 5 \\ - \frac{1}{3} \cdot 5 = k \cdot \frac{5}{5} \\ - \frac{5}{3} = k$

25. anonymous

-15

26. phi

what is -15 ? k is -5/3

27. anonymous

oh i thought you said t multiply -5 into 3 , but what do you do now divide -5/3 into 10

28. phi

you write the formula $y = \frac{k}{x}$ and it might be easier to understand if you write it this way $y = k \cdot \frac{1}{x}$ which means the same thing. now replace k with -5/3 $y = - \frac{5}{3} \cdot \frac{1}{x}$

29. phi

find y when x = 10. that means put in 10 for x in the formula $y = - \frac{5}{3} \cdot \frac{1}{x} \\ y = - \frac{5}{3} \cdot \frac{1}{10}$ and simplify

30. anonymous

y=6

31. phi

if you use a calculator on $- \frac{5}{3} \cdot \frac{1}{10}$ what do you get ?

32. anonymous

-1/6

33. phi

yes, y= -1/6 when x=10. It would be good to be able to do that without the calculator. when you multiply fractions, you multiply top times top and bottom times bottom $- \frac{5}{3} \cdot \frac{1}{10} = - \frac{5 \cdot 1 }{3 \cdot 10}$ we could multiply the bottom 3*10 to get 30 $- \frac{5}{30}$ and then simplify to get -1/6 or, it's easier to notice that 10 is 2*5 $- \frac{5 \cdot 1 }{3 \cdot 10} = - \frac{5 \cdot 1 }{3 \cdot 2 \cdot 5}$ and notice we have a 5 up top and down below, and they simplify to 5/5 = 1 $- \frac{1 }{3 \cdot 2} = - \frac{1}{6}$

34. anonymous

what if x=-4/15 when y=-105,find x when y=4

35. phi

$y = k \cdot \frac{1}{x} \\ -105= k \cdot \frac{1}{-\frac{4}{15}}$

36. phi

multiply both sides by -4/15,

37. anonymous

k=28

38. phi

so $y = \frac{28}{x}$ find x when y=4 replace y with y $4 = \frac{28}{x}$

39. phi

first multiply both sides by x then divide both sides by 4

40. anonymous

7

41. phi

yes. $4 x= \frac{28}{x} \cdot x \\ 4x = 28 \\\frac{4x}{4}= \frac{28}{4} \\x=7$

42. anonymous

thanks are you getting tired of me asking questions

43. phi

no, but I do have to go. make a new post and someone will help you.

44. anonymous

ok thanks