Question

Find the constant of variation k for the inverse variation. Then write an equation for the inverse variation.

y = 2.5 when x = 9


k = 22.5; y = 22.5x





k = 22.5; xy = 22.5


k = 3.6; xy = 3.6

Answer 1

In an inverse variation, the relationship between \( x \) and \( y \) can be expressed as:

\[
y = \frac{k}{x}
\]

or equivalently as:

\[
xy = k
\]

where \( k \) is the constant of variation.

Given that \( y = 2.5 \) when \( x = 9 \), we can find \( k \) by substituting the known values into the equation \( xy = k \):

\[
k = x \cdot y = 9 \cdot 2.5 = 22.5
\]

Now, we can express the equation for the inverse variation:

\[
xy = 22.5
\]

So the correct answer is:

**k = 22.5; xy = 22.5**