The graph shows a proportional relationship between $y$ and $x$, where the line passes through the origin, meaning the ratio between $y$ and $x$ is constant.

To find the constant of proportionality, also known as the slope, we can use the formula: $\text{slope (constant of proportionality)} = \frac{\Delta y}{\Delta x}$ Looking at the graph, we can take two points where the line crosses the grid lines clearly. From the graph, two such points are:

• $(0, 0)$ (the origin),
• $(3, 4)$.

Using these points: $\Delta y = 4 - 0 = 4, \quad \Delta x = 3 - 0 = 3$

Thus, the constant of proportionality is: $\frac{\Delta y}{\Delta x} = \frac{4}{3}$

So, the constant of proportionality is $\frac{4}{3}$.

Would you like more details or have any further questions?

Here are 5 related questions to deepen your understanding:

1. How would the constant of proportionality change if the line were steeper?
2. What is the equation of the line given by this proportional relationship?
3. Can you identify another pair of points that satisfy the same proportional relationship on this graph?
4. How can you interpret the constant of proportionality in a real-world context?
5. If the graph were shifted, would the proportionality still hold? Why or why not?

Tip: Always check if the line passes through the origin in a proportional relationship—this confirms that $y = kx$, where $k$ is the constant.