Question
If y varies directly as x, and y = 2 when x = 8, then the constant of variation is
1/4
4
8
1/8
1/4
4
8
1/8
Answers
GPT-4o mini
If \( y \) varies directly as \( x \), then we can express this relationship as:
\[
y = kx
\]
where \( k \) is the constant of variation.
Given that \( y = 2 \) when \( x = 8 \), we can substitute these values into the equation to find \( k \):
\[
2 = k(8)
\]
To solve for \( k \), we can divide both sides by 8:
\[
k = \frac{2}{8} = \frac{1}{4}
\]
Thus, the constant of variation is:
\[
\boxed{\frac{1}{4}}
\]
\[
y = kx
\]
where \( k \) is the constant of variation.
Given that \( y = 2 \) when \( x = 8 \), we can substitute these values into the equation to find \( k \):
\[
2 = k(8)
\]
To solve for \( k \), we can divide both sides by 8:
\[
k = \frac{2}{8} = \frac{1}{4}
\]
Thus, the constant of variation is:
\[
\boxed{\frac{1}{4}}
\]