To find the equation of the line \( y = mx \) that goes through the origin (0,0) and describes the proportional relationship between the two given points, we first need to determine the slope \( m \) of the line.
Given the points:
- Dot one: (4, 1)
- Dot two: (8, 2)
We can calculate the slope \( m \) using the formula for the slope between two points:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using our points:
- \( (x_1, y_1) = (4, 1) \)
- \( (x_2, y_2) = (8, 2) \)
Plugging in the values:
\[ m = \frac{2 - 1}{8 - 4} = \frac{1}{4} \]
Now that we have the slope, we can write the equation of the line through the origin:
\[ y = \frac{1}{4} x \]
So, the equation of the line that describes the proportional relationship between the given points is:
\[ y = \frac{1}{4} x \]
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