(10, 5)

To find the equation of a proportional relationship that passes through the origin, we can determine the slope \( m \) using the given points.

Using point \( (10, 5) \):
\[ m = \frac{y}{x} = \frac{5}{10} = \frac{1}{2} \]

Using point \( (8, 4) \):
\[ m = \frac{y}{x} = \frac{4}{8} = \frac{1}{2} \]

Using point \( (4, 2) \):
\[ m = \frac{y}{x} = \frac{2}{4} = \frac{1}{2} \]

In all cases, we find that \( m = \frac{1}{2} \). Thus, the equation of the line in slope-intercept form is:
\[ y = \frac{1}{2}x \]

So, the correct answer is:
**B. y = \frac{1}{2}x**