To derive the equation of a line through the origin in the form \( y = mx \), you need to identify the slope of the line on the graph. However, since I can't see the graph, let's consider the given responses in relation to the typical forms of the linear equation \( y = mx \).
- If the slope \( m \) is 8, the line's equation is \( y = 8x \).
- If the slope \( m \) is 1, the equation simplifies to \( y = x \).
- If the slope \( m \) is 3, the equation is \( y = 3x \).
The options given include potentially simplified forms for these slopes (like \( y = \frac{3}{3}x \), which simplifies to \( y = x \)).
To summarize:
- The line through the origin will have an equation of the form \( y = mx \).
- If the slope is 8, choose \( y = 8x \).
- If the slope is 1, choose \( y = x \).
- If the slope is 3, choose \( y = 3x \).
Given the responses:
- \( y = 8x \)
- \( y = x \)
- \( y = 3x \)
- \( y = \frac{3}{3}x \) (which simplifies to \( y = x \))
Select the appropriate option based on the slope observed in the graph. If no specific slope is mentioned or shown, you can choose one of the given equations accordingly.
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