Question

The values of x and y vary directly and one pair of values are given write an equation that relates x and y simplify completely X=12 y=3

Answer 1

Given that x varies directly with y, we have that:

`x\text{ }\alpha\text{ y}`

Now, we replace the sign of proportionality with the contant k, as follows:

`x=ky`

Now, since we have a pair of values already given for x and y, we directly substitute those values into the equation above in order to obtain the value of the constant, as shown below:

`\begin{gathered} x=12\text{ and y = 3} \\ \end{gathered}`

Thus:

`\begin{gathered} x=ky \\ 12=k(3) \\ (12)/(3)=(k(3))/(3) \\ 4=k \end{gathered}`

Thus, we have the value of the constant k to be equal to 4.

Now, we have the equation to be:

`\begin{gathered} x=ky \\ x=4y \end{gathered}`

Finally, we make y the subject, as follows:

`\begin{gathered} x=4y \\ (x)/(4)=(4y)/(4) \\ (x)/(4)=y \end{gathered}`

Therefore:

`y=(x)/(4)`

or:

`y=(1)/(4)x`

The value that goes into the numerator in the i