To find the equation of the line \( y = mx \) that passes through the origin and describes the relationship between the two points given, we first need to determine the slope \( m \) of the line.
We have two points:
- Point 1: \( (1, 4) \)
- Point 2: \( (2, 8) \)
The slope \( m \) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the coordinates of the points:
- \( (x_1, y_1) = (1, 4) \)
- \( (x_2, y_2) = (2, 8) \)
Now substituting in the values:
\[ m = \frac{8 - 4}{2 - 1} = \frac{4}{1} = 4 \]
Thus, the slope \( m \) is \( 4 \).
The equation of the line through the origin can now be written as:
\[ y = 4x \]
So, the equation for the line describing the relationship between the two points is:
\[ y = 4x \]
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