IXL - Write and solve inverse variation equations (Algebra 1 practice)

or

If
y
varies
inversely
with
x
and
y = 1
when
x = 4
,
find
y
when
x = 2
.

Write and solve an inverse variation equation to find the answer.

y =

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or

Learn with an example

question

Assume
that
y
varies
inversely
with
x .
If
y = 4
when
x = 3
,
find
y
when
x = 1
.

Write and solve an inverse variation equation to find the answer.

y =

key idea

Inverse variation
can
be
represented
by
the
equation
y
=
k
x
or
xy = k
.

The variable k is known as the constant of variation, and it cannot equal zero.

solution

First
find
the
constant
of
variation.
Plug
x = 3
and
y = 4
into
the
inverse
variation
equation
and
then
solve
for
k .

xy

=

k

(3)(4)

=

k

12

=

k

Now
use
k
=
12
to
write
the
inverse
variation
equation.

y

=

k

x

y

=

12

x

The
inverse
variation
equation
is
y
=
12
x
.
This
can
also
be
written
as
xy = 12
.

Finally,
use
the
inverse
variation
equation
to
find
y
when
x = 1
.
It
is
easiest
to
use
the
first
equation,
y
=
12
x
.

y

=

12

x

y

=

12

1

y

=

12

So,
y = 12
.

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