Question

13.
Suppose that y varies inversely with x. Write an equation for the inverse variation.

y = 6 when x = 8

Answer 1

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 \( x \).