Question

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

y = 5 when x = 7.5


k = 15; xy = 1.5








k = 37.5; y = 37.5x

Answer 1

In inverse variation, we have the relationship:

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

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

Given that \( y = 5 \) when \( x = 7.5 \), we can find \( k \) by substituting these values into the equation:

\[ 5 = \frac{k}{7.5} \]

To solve for \( k \), we can multiply both sides by 7.5:

\[ k = 5 \times 7.5 \]

Calculating that gives:

\[ k = 37.5 \]

Now, we can write the equation for the inverse variation using the value of \( k \):

\[ y = \frac{37.5}{x} \]

So, the constant of variation \( k \) is 37.5, and the equation for the inverse variation is:

\[ y = \frac{37.5}{x} \]