To find the equation of the line \( y = mx \) that passes through the origin and describes a proportional relationship between the points (1, 4) and (2, 8), we first need to determine the slope \( m \).
In a proportional relationship, if \( (x_1, y_1) = (1, 4) \) and \( (x_2, y_2) = (2, 8) \), we can compute the slope \( m \) using the coordinates of one of the points:
Using the first point (1, 4): \[ m = \frac{y_1}{x_1} = \frac{4}{1} = 4 \]
Now, using the second point (2, 8) to confirm the slope: \[ m = \frac{y_2}{x_2} = \frac{8}{2} = 4 \]
Since we calculated the same slope from both points, we can conclude that the slope \( m \) is indeed 4.
Therefore, the equation of the line is: \[ y = 4x \]
This describes the proportional relationship through the origin for the given points.
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