Question

Identify the proportional relationship from the graph points
Line A(0,0), (2,2), over 2 units (4,2) up (6,4)
Line B (2,2), (6,6)
Live C is an arch with no real points
Line D (0,2), (2,4),(3,5)

Answer 1

To identify which of the lines represents a proportional relationship, we need to look for a straight line that passes through the origin, as proportional relationships can be expressed in the form \( y = kx \) where \( k \) is a constant.

Let's analyze the lines based on your description:

- **Line A**:
- Points: (0,0), (2,2), (4,2), (6,4)
- This line starts at the origin (0,0) and shows both vertical and horizontal movement, indicating that it is not a straight line through the origin since it does not maintain a consistent ratio as you move away from the origin.

- **Line B**:
- Points: (2,2), (6,6)
- This line does not pass through the origin, since (2,2) is not (0,0). However, if you extend the line backwards, it could theoretically go through the origin, implying a proportional relationship.

- **Line C**:
- It is described as an arch, which typically indicates a non-linear relationship. This would not represent a proportional relationship.

- **Line D**:
- Points: (0,2), (2,4), (3,5)
- This line does not pass through the origin (0,2) and therefore cannot be proportional either.

Based on this analysis, it appears that **Line B** is the only one that has a possibility of being proportional because it could represent a linear relationship if extended appropriately. However, since it does not actually pass through the origin, it strictly does not meet the criteria for being classified as a proportional relationship.

**Conclusion**: None of the lines represent a strict proportional relationship based on the provided point descriptions. If you consider only strict mathematical definitions, there is no valid choice among the given lines. Line B is close but doesn't technically count.