Question
if there is inverse variation y=6 when x=-2, find y when x=-3
Answers
GPT-4o mini
In inverse variation, the relationship between \( x \) and \( y \) can be expressed as:
\[
y = \frac{k}{x}
\]
where \( k \) is a constant.
Given that \( y = 6 \) when \( x = -2 \), we can find the constant \( k \):
\[
6 = \frac{k}{-2}
\]
Multiplying both sides by -2 gives:
\[
k = 6 \times -2 = -12
\]
Now that we have \( k = -12 \), we can use it to find \( y \) when \( x = -3 \):
\[
y = \frac{-12}{-3} = 4
\]
Thus, when \( x = -3 \), \( y \) is \( 4 \).
\[
y = \frac{k}{x}
\]
where \( k \) is a constant.
Given that \( y = 6 \) when \( x = -2 \), we can find the constant \( k \):
\[
6 = \frac{k}{-2}
\]
Multiplying both sides by -2 gives:
\[
k = 6 \times -2 = -12
\]
Now that we have \( k = -12 \), we can use it to find \( y \) when \( x = -3 \):
\[
y = \frac{-12}{-3} = 4
\]
Thus, when \( x = -3 \), \( y \) is \( 4 \).