Question

10.
Suppose that y varies inversely with x. Write an equation for the inverse variation.

y = 4 when x = 6

Answer 1

Since \( y \) varies inversely with \( x \), we can express this relationship using the equation:

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

where \( k \) is a constant.

To find the value of \( k \), we can use the given information: \( y = 4 \) when \( x = 6 \).

Substituting these values into the equation gives:

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

To solve for \( k \), we can multiply both sides by 6:

\[
k = 4 \cdot 6 = 24
\]

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

\[
y = \frac{24}{x}
\]

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