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 = 3.6; xy = 3.6


k = 22.5; y = 22.5x





k = 22.5; xy = 22.5

Answer 1

In an inverse variation, the relationship can be expressed as:

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

Where \( k \) is the constant of variation. To find \( k \), we can use the given values of \( y \) and \( x \).

Given:
- \( y = 2.5 \)
- \( x = 9 \)

We can find \( k \) by rearranging the equation:

\[ k = xy \]

Now we substitute the values:

\[ k = 2.5 \cdot 9 \]

Calculating that gives us:

\[ k = 22.5 \]

Thus, the constant of variation is \( k = 22.5 \).

Now we can write the equation for the inverse variation:

\[ y = \frac{22.5}{x} \]

So, the correct answer is:

**k = 22.5; xy = 22.5**