Question

12.
Suppose that y varies inversely with x. Write an equation for the inverse variation.

y = 4 when x = 7

Answer 1

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

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

where \( k \) is a constant.

Given that \( y = 4 \) when \( x = 7 \), we can substitute these values into the equation to find \( k \):

\[
4 = \frac{k}{7}
\]

To solve for \( k \), we multiply both sides by 7:

\[
k = 4 \times 7 = 28
\]

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

\[
y = \frac{28}{x}
\]

This is the equation representing the inverse variation of \( y \) with respect to \( x \).