Certainly! To solve this problem, let's follow a series of logical steps. We know that when two variables vary directly, their ratio remains constant. In this case, we understand that \(\( y \)\) varies directly with \(\( x \)\).
1. Determine the constant of variation (k):
- Direct variation means \(\( y = kx \)\), where \(\( k \)\) is the constant of proportionality.
- Given \(\( y = 70 \)\) when \(\( x = 14 \)\), we can identify \(\( k \)\) by substituting these values into the direct variation equation:
\(\[
70 = k \cdot 14
\]\)
- Solving for \(\( k \)\), we divide both sides by 14:
\(\[
k = \frac{70}{14} = 5
\]\)
2. Use the constant of variation to find the new value of \(\( y \)\):
- Now that we know the constant \(\( k \)\), we can use it to find \(\( y \)\) when \(\( x = 3 \)\).
- Substitute \(\( k = 5 \)\) and \(\( x = 3 \)\) into the direct variation equation:
\(\[
y = kx = 5 \cdot 3
\]\)
- Hence, we find:
\(\[
y = 15
\]\)
So, when \(\( x = 3 \)\), \(\( y \)\) is \(\( 15 \)\).
