# If y varies directly as x, and y=42 as x=6, how do you find y for the x-value 3?

Jun 3, 2015

Direct variation can be represented as:
$\frac{x}{y} = k$
where color(green)(k is the constant

$x = 6 \mathmr{and} y = 42$
so substituting :
$\frac{6}{42} = k$
 color(green)(k = 1/7

Now, we have the value of $\textcolor{g r e e n}{k}$ and $x = 3$ , substituting these in the variation to find $y$
$\frac{x}{\textcolor{red}{y}} = k$

$\frac{3}{\textcolor{red}{y}} = \frac{1}{7}$

By cross multiplying we get
 color(red)(y = 21

on observing the values

• when $x = 6 , \textcolor{red}{y} = \textcolor{g r e e n}{7} \times 6 = 42$
• when $x = 3 , \textcolor{red}{y} = \textcolor{g r e e n}{7} \times 3 = 21$

 color(red)(y is always $7$ times $x$ , as the constant color(green)(k = 7