13.

Suppose that y varies inversely with x. Write an equation for the inverse variation.

y = 6 when x = 8

1 answer

When \( y \) varies inversely with \( x \), the relationship can be expressed using the equation:

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

where \( k \) is a constant.

Given that \( y = 6 \) when \( x = 8 \), we can find the constant \( k \) by substituting these values into the equation:

\[ 6 = \frac{k}{8} \]

To solve for \( k \), multiply both sides by 8:

\[ k = 6 \times 8 = 48 \]

Now that we have the constant \( k \), we can write the equation for the inverse variation:

\[ y = \frac{48}{x} \]

This is the equation that expresses the inverse variation between \( y \) and \( x \).