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:

$\begin{gathered} x=ky \\ 12=k(3) \\ \frac{12}{3}=\frac{k(3)}{3} \\ 4=k \end{gathered}$

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:

$\begin{gathered} x=4y \\ \frac{x}{4}=\frac{4y}{4} \\ \frac{x}{4}=y \end{gathered}$

Therefore:

$y=\frac{x}{4}$

or:

$y=\frac{1}{4}x$

The value that goes into the numerator in the i