SOLUTION: Direct and Indirect Variation. I do not understand how to solve this or any problems such as these. y varies directly with x. y =15 when x=4. what is the value of y when x=5

Question 618635: Direct and Indirect Variation. I do not understand how to solve this or any problems such as these.
y varies directly with x. y =15 when x=4. what is the value of y when x=5
or y varies inversely with x y=8 when x=8. what is the value of y when x=4
Found 3 solutions by richwmiller, nerdybill, MathTherapy:
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
direct
y=kx
15=k4
15/4=k
y=5*15/4
y=75/4
indirect
y=x/k
8=8/k
k=1
y=x/1
y=5/1
y=5

Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
y varies directly with x. y =15 when x=4. what is the value of y when x=5
.
When you see "y varies directly with x" think:
y = kx (where k is a constant)
find this constant by plugging in "y =15 when x=4" from the problem:
15 = k(4)
15/4 = k
.
Now, our equation is:
y = (15/4)X
We can now answer:
what is the value of y when x=5
y = (15/4)X
y = (15/4)5
y = 75/4
y = 18.75
.
y varies inversely with x y=8 when x=8. what is the value of y when x=4
When you see "y varies inversely with x" think:
y = k/x (where k is a constant)
find this constant by plugging in "y=8 when x=8" from the problem:
8 = k/8
8/8 = k
1 = k
.
Now our equation is:
y = 1/x
We can now answer:
what is the value of y when x=4
y = 1/x
y = 1/4
y = .25

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Direct and Indirect Variation. I do not understand how to solve this or any problems such as these.
y varies directly with x. y =15 when x=4. what is the value of y when x=5
or y varies inversely with x y=8 when x=8. what is the value of y when x=4

Direct
y = kx

----- Substituting 15 for y, and 4 for x

4k = 15

k (constant of variation) =

y = kx

----- Substituting for k, and 5 for x

, or

Inverse or Indirect
y = k/x

----- Substituting 8 for y, and 8 for x

k (constant of variation) =

y = k/x

----- Substituting 64 for k, and 4 for x

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