To derive the equation of a line through the origin (0, 0) in the form \(y = mx\), we need to identify the slope \(m\) of the line. The slope can be derived from the graph by finding two points on the line and calculating the change in \(y\) over the change in \(x\).
From your options, here are the interpretations:
- \(y = 8x\) implies a slope of 8.
- \(y = x\) implies a slope of 1.
- \(y = 3x\) implies a slope of 3.
If we are looking for a specific equation based on a slope that corresponds to the data shown on a graph, you should assess which equation best fits the slope from the graph.
If the slope is not specified, you can select based on the values:
- For \(y = 8x\), the line will rise quickly.
- For \(y = x\), the line will rise at a 45-degree angle.
- For \(y = 3x\), the line will rise moderately.
Thus, the equation will depend on the specific slope you observe in the graph.
Please refer to the graph to determine which equation is the best fit and select the appropriate choice based on the slope. If the slope appears to be 3, the simplified form would be \(y = 3x\). If the slope is 1, it would be \(y = x\) and so on.
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