https://file.aiquickdraw.com/mathbot/file/1730021507352o3mdvtm4.jpg

To analyze this graph and its options, let’s look at each detail:

1. **Graph Analysis**:
   - The graph shows a relationship between the number of hours (x-axis) and the cost of bike hire in AED (y-axis).
   - It does not pass through the origin \((0, 0)\), as the line of points does not start from zero.
   - The spacing of points along the y-axis suggests that the rate of change is not constant; this is because the increments in cost do not increase by the same amount for each hour.

2. **Options Analysis**:
   - **"If you draw a line through the points, it does not pass through the origin (0, 0)."** - **True** because the graph does not start from the origin.
   - **"The rate of change is not constant."** - **True** as the y-values do not increase by the same amount for each hour.
   - **"If you draw a line through the points, it passes through the origin (0, 0)."** - **False** based on the graph.
   - **"The relationship is not linear."** - **True** because the points do not form a straight line.
   - **"This is a proportional relationship because the ratios \( \frac{y}{x} \) are all equivalent."** - **False** as the ratio \( \frac{y}{x} \) varies for different points, meaning it’s not proportional.
   - **"The ratios \( \frac{y}{x} \) are not equivalent for all points."** - **True** because each point has a different \( \frac{y}{x} \) ratio.

3. **Correct Choices**:
   - The two correct answers are:
     - **"If you draw a line through the points, it does not pass through the origin (0, 0)."**
     - **"The rate of change is not constant."**

Would you like more details on any of these steps?

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### Related Questions:
1. What does a proportional relationship look like on a graph?
2. How can you identify if a relationship is linear based on a graph?
3. Why does a line passing through the origin indicate a proportional relationship?
4. What does it mean for the rate of change to be constant in a graph?
5. How does a non-linear graph affect the interpretation of a relationship?

### Tip:
For a proportional relationship, the graph should form a straight line passing through the origin, with a constant rate of change.

This graph shows the relationship between the cost of bike hire and the number of hours. Choose all that apply. Select 2 choices.

Explore the relationship between bike hire cost and hours on a graph. Identify key mathematical concepts like rate of change and proportionality, suitable for middle school students. Learn to interpret graphs and recognize non-linear and non-proportional relationships.

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