To determine which equations represent non-proportional relationships, we look for equations that do not represent a straight line through the origin (0,0) or those that include a constant term added to the product of a variable (i.e., y = mx + b where b ≠ 0).
- y = 5x − 9 - This is non-proportional because it has a constant term (-9).
- y = 23x - This is proportional because it can be rewritten as y = mx with m = 23, and there is no constant term.
- y = 4.08x - This is also proportional, similar to above.
- y = 10x + 10 - This is non-proportional because it has a constant term (+10).
- y = −15x - This is proportional for the same reason as above.
- y = x² - This is non-proportional because it represents a quadratic relationship, not a linear one.
Based on this analysis, the three equations that represent non-proportional relationships are:
- y = 5x − 9 (non-proportional)
- y = 10x + 10 (non-proportional)
- y = x² (non-proportional)
So the correct responses would be:
- y = 5x − 9
- y = 10x + 10
- y = x²