To find the equation of the line in the form \( y = mx \) that passes through the origin and represents the proportional relationship defined by the points (1, 3) and (2, 6), we first need to determine the slope \( m \) of the line.
The slope \( m \) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (1, 3) and (2, 6):
\[ y_1 = 3, , y_2 = 6, , x_1 = 1, , x_2 = 2 \]
Substituting in the values:
\[ m = \frac{6 - 3}{2 - 1} = \frac{3}{1} = 3 \]
Now that we have the slope \( m \), we can write the equation of the line:
\[ y = mx \implies y = 3x \]
Thus, the equation of the line that represents the proportional relationship through the origin is:
\[ y = 3x \]