If there is inverse variation and y=-4 when x=14, find x when y=28.

1 answer

In inverse variation, the relationship between \( x \) and \( y \) can be expressed as:

\[ xy = k \]

where \( k \) is a constant.

Given that \( y = -4 \) when \( x = 14 \), we can find \( k \) as follows:

\[ k = xy = 14 \times (-4) = -56 \]

Now that we have \( k = -56 \), we can find \( x \) when \( y = 28 \) using the inverse variation formula:

\[ xy = k \] \[ x \cdot 28 = -56 \]

To find \( x \), we can solve for it:

\[ x = \frac{-56}{28} = -2 \]

Thus, when \( y = 28 \), \( x \) is \( -2 \).