Let's analyze the graph to write an equation for the proportional relationship.

1. Identifying the constant of proportionality (slope): The line passes through the origin (0, 0), indicating that the relationship is proportional. By checking the coordinates of two points on the line, we can calculate the slope, which is the constant of proportionality.

   From the graph:

   • One point is at (10, 10).
   • Another point is at (20, 20).

2. Calculate the slope (constant of proportionality): The formula for slope is: $\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points (10, 10) and (20, 20): $\text{slope} = \frac{20 - 10}{20 - 10} = \frac{10}{10} = 1$

3. Writing the equation: Since the slope is 1, the equation of the line is: $y = 1x$ Simplifying: $y = x$

This is the equation that represents the proportional relationship shown in the graph.

Would you like more details, or do you have any questions about the solution?

Here are 5 related questions to deepen your understanding:

1. What happens to the equation if the line has a different slope?
2. How can you find the slope if the line does not pass through the origin?
3. How does the y-intercept affect the equation of a line?
4. What is the relationship between the slope and the steepness of the line?
5. Can you derive an equation for a non-proportional linear relationship from a graph?

Tip: Always pick two points as far apart as possible on a graph to ensure greater accuracy when calculating the slope.