Question

If y varies inversely with x, and the constant of variation

is 4.5, what are the values missing in the table?

Answer 1

`A=0.5`

`B=4.5`

`C=1.5`

`D=0.5`

Step-by-step explanation:

The form an the equation of inverse variation is:

`y=(k)/(x)`

Being "k" the constant of variation.

Since we know "k" and we have the values given in the table, we can find the missing values:

To find A we need to substitute the
`y=9`, the value of "k" and
`x=A` into the equation and solve for "A":

`9=(4.5)/(A)`

`A=(4.5)/(9)=0.5`

To find B we need to substitute the
`x=1`, the value of "k" and
`y=B` into the equation:

`B=(4.5)/(1)=4.5`

To find C we need to substitute the
`y=3`, the value of "k" and
`x=C` into the equation and solve for "C":

`3=(4.5)/(C)`

`C=(4.5)/(3)=1.5`

To find D we need to substitute the
`x=9`, the value of "k" and
`y=D` into the equation:

`D=(4.5)/(9)=0.5`

Answer 2

A. 0.5

B. 4.5

C. 1.5

D. 0.5

Explanation:

y varies inversely with x can be written as:

y = k/x

where k is constant of variation.

1. value of A

x=A, y = 9 and k = 4.5 (given)

y = k/x

9 = 4.5/A

=> A = 4.5/9

=> A=0.5

2. Value of B

x =1, y= B, k = 4.5

y = k/x

B = 4.5/1

B= 4.5

3. Value of C

x=C, y=3. k=4.5

y = k/x

3 = 4.5/C

3C = 4.5

C = 4.5/3

C = 1.5

4. Value of D

x= 9, y=D, k=4.5

y = k/x

D = 4.5/9

D = 0.5