https://file.aiquickdraw.com/mathbot/file/1726584886303p480myfd.jpg

The graph shows a linear relationship, and the problem asks for the equation representing the proportional relationship between \( y \) and \( x \).

### Step 1: Identify the form of the equation
For a proportional relationship, the equation has the form:
\[
y = kx
\]
where \( k \) is the constant of proportionality (the slope of the line).

### Step 2: Determine the slope \( k \)
To find \( k \), we need two points from the graph. The graph appears to pass through:
- \( (0, 0) \) (the origin)
- \( (10, 2) \)

Now, calculate the slope \( k \):
\[
k = \frac{\Delta y}{\Delta x} = \frac{2 - 0}{10 - 0} = \frac{2}{10} = 0.2
\]

### Step 3: Write the equation
The equation of the line is:
\[
y = 0.2x
\]

Let me know if you'd like further details or if you have any questions.

### Related Questions:
1. What happens to the slope if the line is steeper?
2. How would the equation change if the line passed through a different point?
3. Can you explain what the slope represents in this context?
4. What is the significance of the line passing through the origin?
5. How do you find the slope if the points aren't clear from the graph?

**Tip:** The slope of a line represents how much \( y \) changes for each unit increase in \( x \).

Find the equation that represents the proportional relationship in this graph, for y in terms of x.

Learn how to find the equation of a proportional relationship from a graph by determining the slope and writing the equation y = kx. This problem uses basic algebra and graphical analysis, suitable for students in Grades 6-8.

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