Answer:
y = 8
Step-by-step explanation:
Given that y is directly proportional to x² then the equation relating them is
y = kx² ← k is the constant of variation
To find k use the condition y = 2 when x = 3, then
2 = k × 3² = 9k ( divide both sides by 9 )
[tex]\frac{2}{9}[/tex] = k
y = [tex]\frac{2}{9}[/tex] x² ← equation of proportion
When x = 6, then
y = [tex]\frac{2}{9}[/tex] × 6² = [tex]\frac{2}{9}[/tex] × 36 = 2 × 4 = 8
