Question

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

y = 4.5 when x = 3


k = 13.5; 13.5 y = x


k = 1.5; y = 1.5 x


k = 13.5; xy = 13.5


k = 1.5; y =

Answer 1

In inverse variation, the relationship between \( x \) and \( y \) can be described by the equation:

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

where \( k \) is a constant. To find the constant of variation \( k \), we can use the given values \( y = 4.5 \) when \( x = 3 \).

Substituting the values into the equation:

\[
4.5 = \frac{k}{3}
\]

To solve for \( k \), multiply both sides by 3:

\[
k = 4.5 \times 3
\]

Calculating this gives:

\[
k = 13.5
\]

Now that we have the constant of variation, we can write the equation for the inverse variation as follows:

\[
xy = 13.5
\]

Thus, the correct options are:

**k = 13.5; xy = 13.5**