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To find the equation of the line \( y = mx \), we need to determine the slope \( m \) based on the points provided on the graph. The graph shows a proportional relationship, meaning the line passes through the origin \((0,0)\) and the slope \( m \) can be calculated as the ratio of the change in \( y \) over the change in \( x \) between two points on the line.

From the image, we can extract the coordinates of two points:
- Point 1: \( (1, 3) \)
- Point 2: \( (2, 6) \)

The formula for the slope \( m \) is:

\[
m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the coordinates:

\[
m = \frac{6 - 3}{2 - 1} = \frac{3}{1} = 3
\]

Thus, the equation of the line is:

\[
y = 3x
\]

Would you like more details or have any questions?

### Related questions:
1. How would the equation change if the slope were negative?
2. How can you verify the equation of the line using additional points from the graph?
3. What is the significance of the line passing through the origin in this context?
4. Can you find the slope of a line without using graph points?
5. How would you find the equation of a line if the relationship weren't proportional?

**Tip**: When finding the slope from a graph, choose points with clear integer values to avoid rounding errors.

Find the equation of the line y = mx through the origin that describes the proportional relationship shown in the graph.

Learn how to find the equation of a line passing through the origin using proportional relationships. This step-by-step guide explains how to calculate the slope from two points on a line and derive the equation in the form y = mx. Suitable for students in Grades 7-9.

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