Question

Each graph below shows a relationship between and .
For each graph, determine whether and are proportional.
If and are proportional, fill in the blank with a number in simplest form.

Graph 1
y12345678910x123456789100
Proportional
is

Not proportional
Graph 2
y12345678910x123456789100
Proportional
is

Not proportional
Graph 3
y12345678910x123456789100
Proportional
is

Not proportional

Answer 1

To determine whether the variables \( y \) and \( x \) are proportional in the graphs you mentioned, we check if the ratio \( \frac{y}{x} \) is constant for all points on the graph.

1. **Graph 1**:
- If the graph is a straight line passing through the origin (0, 0), then \( y \) and \( x \) are proportional.
- If you find specific points and see they follow a constant ratio, you can determine \( k \) where \( y = kx \).
- If not, then they are not proportional.

2. **Graph 2**:
- Check the same way as for Graph 1.
- Look for linearity through the origin.

3. **Graph 3**:
- Again, apply the same reasoning.

### Example Analysis:
If all three graphs are proportional with the values being as follows for each:

- For **Graph 1**: Suppose the ratio \( \frac{y}{x} \) is 2 when calculating from points, then:
- Proportional: \( k \) is \( 2 \).

- For **Graph 2**: If the ratio \( \frac{y}{x} \) is 3, then:
- Proportional: \( k \) is \( 3 \).

- For **Graph 3**: If the graph indicates that it does not pass through the origin or the ratio is inconsistent:
- Not Proportional.

To accurately fill in those fields, observe the graphs and use the points to confirm the relationships and compute the ratios. If they yield a constant ratio, state it as \( k \); otherwise, indicate they are not proportional.

Feel free to provide specific points from the graphs if you need further assistance in calculations or ratios!