Question

9.
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 with the equation:

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

where \(k\) is a constant.

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

Plugging in those values into the equation:

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

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

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

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

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

Thus, the equation for the inverse variation is:

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