Question

if there is inverse variation y=-5 when x=2, find y when x=-6

Answer 1

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 \( x = -6 \), \( y = \frac{5}{3} \).