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

Question

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

1 Answer

Impact of this question

13244 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-03T08:12:47

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

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

Now, we have the value of $k$ $color(green)(k)$ and $x = 3$ $x = 3$ , substituting these in the variation to find $y$ $y$
$\frac{x}{y} = k$ $x/color(red)(y) = k$

$\frac{3}{y} = \frac{1}{7}$ $3/color(red)(y )= 1/7$

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

on observing the values

when $x = 6, y = 7 \times 6 = 42$ $x = 6 , color(red)(y) = color(green)(7)xx6= 42$
when $x = 3, y = 7 \times 3 = 21$ $x = 3 , color(red)(y) = color(green)(7)xx3 = 21$

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

Science

Math

Humanities

... and beyond

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

1 Answer

Related questions

Impact of this question