To find the equation of the line in the form \( y = mx \) that passes through the origin and describes the proportional relationship shown in the graph, we first need to determine the slope \( m \) of the line.
The points given are \( (1, 4) \) and \( (2, 8) \).
To calculate the slope \( m \), we use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the coordinates of the points:
\[ m = \frac{8 - 4}{2 - 1} = \frac{4}{1} = 4 \]
Now that we have the slope, the equation of the line through the origin is:
\[ y = 4x \]
Thus, the equation of the line that describes the proportional relationship shown in the graph is:
\[ y = 4x \]