Question
Which THREE equations represent non-proportional relationships?(1 point)
Responses
y=5x−9
y is equal to the fraction with numerator 5 and denominator x minus 9
y=23x
y is equal to 2 thirds x
y=4.08x
y is equal to 4 point 0 8 x
y=10x+10
y is equal to 10 x plus 10
y=−15x
y is equal to negative 15 x
y=x2
Responses
y=5x−9
y is equal to the fraction with numerator 5 and denominator x minus 9
y=23x
y is equal to 2 thirds x
y=4.08x
y is equal to 4 point 0 8 x
y=10x+10
y is equal to 10 x plus 10
y=−15x
y is equal to negative 15 x
y=x2
Answers
GPT-4o mini
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).
1. **y = 5x − 9** - This is non-proportional because it has a constant term (-9).
2. **y = 23x** - This is proportional because it can be rewritten as y = mx with m = 23, and there is no constant term.
3. **y = 4.08x** - This is also proportional, similar to above.
4. **y = 10x + 10** - This is non-proportional because it has a constant term (+10).
5. **y = −15x** - This is proportional for the same reason as above.
6. **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:
1. **y = 5x − 9** (non-proportional)
2. **y = 10x + 10** (non-proportional)
3. **y = x²** (non-proportional)
So the correct responses would be:
- y = 5x − 9
- y = 10x + 10
- y = x²
1. **y = 5x − 9** - This is non-proportional because it has a constant term (-9).
2. **y = 23x** - This is proportional because it can be rewritten as y = mx with m = 23, and there is no constant term.
3. **y = 4.08x** - This is also proportional, similar to above.
4. **y = 10x + 10** - This is non-proportional because it has a constant term (+10).
5. **y = −15x** - This is proportional for the same reason as above.
6. **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:
1. **y = 5x − 9** (non-proportional)
2. **y = 10x + 10** (non-proportional)
3. **y = x²** (non-proportional)
So the correct responses would be:
- y = 5x − 9
- y = 10x + 10
- y = x²