Let's analyze each graph to determine if $x$ and $y$ are proportional.

Graph 1:

In Graph 1, we observe that the line passes through the origin (0,0) and forms a straight line. This suggests a proportional relationship between $x$ and $y$.

• The slope of the line gives us the constant of proportionality. From the graph, when $x = 2$, $y = 6$. The ratio $\frac{y}{x} = \frac{6}{2} = 3$, so $y$ is 3 times $x$.

Thus, Graph 1 is proportional, and the relationship is $y = 3x$.

Graph 2:

In Graph 2, the line does not pass through the origin, which is a key requirement for proportionality. Even though the line is straight, the fact that it doesn't pass through the origin means that $x$ and $y$ are not proportional.

Thus, Graph 2 is not proportional.

Graph 3:

In Graph 3, the graph shows a vertical line. This means that the value of $x$ remains the same (specifically $x = 2$) while $y$ changes. This clearly indicates there is no proportional relationship between $x$ and $y$.

Thus, Graph 3 is not proportional.

Conclusion:

1. Graph 1: Proportional, $y = 3x$
2. Graph 2: Not proportional
3. Graph 3: Not proportional

Would you like more details or have any questions?

Here are 5 follow-up questions to expand on this information:

1. How can we find the constant of proportionality from a graph?
2. Why must a proportional relationship pass through the origin?
3. How does the slope of the line relate to proportionality?
4. Can a non-linear graph ever represent a proportional relationship?
5. How can we check proportionality algebraically from given points?

Tip: A proportional relationship is always represented by a straight line passing through the origin. Keep an eye on both these conditions!