Question
If there is inverse variation and y=24 when x=2, find y when x=-4.
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 \( y = 24 \) when \( x = 2 \), we can find \( k \):
\[
24 = \frac{k}{2}
\]
Multiplying both sides by 2, we get:
\[
k = 24 \times 2 = 48
\]
Now that we have \( k \), we can find \( y \) when \( x = -4 \):
\[
y = \frac{k}{x} = \frac{48}{-4}
\]
Calculating this gives:
\[
y = -12
\]
Therefore, when \( x = -4 \), \( y = -12 \).
\[
y = \frac{k}{x}
\]
where \( k \) is a constant.
Given that \( y = 24 \) when \( x = 2 \), we can find \( k \):
\[
24 = \frac{k}{2}
\]
Multiplying both sides by 2, we get:
\[
k = 24 \times 2 = 48
\]
Now that we have \( k \), we can find \( y \) when \( x = -4 \):
\[
y = \frac{k}{x} = \frac{48}{-4}
\]
Calculating this gives:
\[
y = -12
\]
Therefore, when \( x = -4 \), \( y = -12 \).