In inverse variation, we can express the relationship between \( x \) and \( y \) using the equation:
\[ xy = k \]
where \( k \) is a constant.
Given that \( y = -5 \) when \( x = 2 \), we can find \( k \):
\[ k = xy = (2)(-5) = -10 \]
Now we need to find \( y \) when \( x = -6 \). We use the value of \( k \) we just calculated:
\[ xy = k \quad \Rightarrow \quad (-6)y = -10 \]
To solve for \( y \), divide both sides by -6:
\[ y = \frac{-10}{-6} = \frac{10}{6} = \frac{5}{3} \]
Thus, when \( x = -6 \), \( y = \frac{5}{3} \).
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