To determine which equations represent non-proportional relationships, we look for equations that do not have the form of \( y = kx \) (where \( k \) is a constant) or that include a constant term besides the product of \( k \) and \( x \).
Here are the given equations analyzed:
- \( y = 4.08x \) - This is a proportional relationship.
- \( y = -15x \) - This is also a proportional relationship.
- \( y = x^2 \) - This is a non-proportional relationship because it is not in the form \( y = kx \).
- \( y = 10x + 10 \) - This is non-proportional because of the additional constant (10).
- \( y = \frac{2}{3}x \) - This is a proportional relationship.
- \( y = \frac{5}{x} - 9 \) - This is a non-proportional relationship due to the inverse relationship and the constant (-9).
Based on this analysis, the three equations that represent non-proportional relationships are:
- \( y = x^2 \)
- \( y = 10x + 10 \)
- \( y = \frac{5}{x} - 9 \)