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To find the equation of the line \( y = mx \) that passes through the origin, we need to determine the slope \( m \) of the line.

### Step 1: Identify Points on the Line
From the graph, two clear points on the line are:
1. \( (1, 3) \)
2. \( (3, 9) \)

### Step 2: Calculate the Slope \( m \)
The slope \( m \) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (1, 3) \) and \( (3, 9) \):
- \( x_1 = 1 \), \( y_1 = 3 \)
- \( x_2 = 3 \), \( y_2 = 9 \)

Substitute these values into the slope formula:
\[
m = \frac{9 - 3}{3 - 1} = \frac{6}{2} = 3
\]

### Step 3: Write the Equation of the Line
Since the line passes through the origin and has a slope \( m = 3 \), the equation of the line is:
\[
y = 3x
\]

### Final Answer
The equation of the line is:
\[
y = 3x
\]

Would you like further details or explanations on any part of this process?

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Here are some related questions to deepen your understanding:
1. How do you calculate the slope if the line does not pass through the origin?
2. What changes in the equation if the line has a negative slope?
3. How can you determine the slope of a line by only looking at its graph?
4. What would be the equation of a line parallel to this line that passes through a different point?
5. How can you find the equation of a line given two arbitrary points?

**Tip:** For lines passing through the origin, the y-intercept is always zero, simplifying the equation to \( y = mx \).

The graph shows the proportional relationship. Derive the equation of the line y = mx through the origin.

Learn how to derive the equation of a line y = mx through the origin using points from a graph. This problem covers concepts of linear equations, slope calculation, and proportional relationships. Suitable for students in Grades 7-9.

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