To determine the equation of the line that passes through the origin and touches the right triangle with a base of 8 units and a height of 5 units, we start by identifying the slope of the line.
The right triangle has its vertex at the origin (0, 0), one vertex at (8, 0), and the other vertex at (0, 5). The slope of the line \( m \) going from the origin (0, 0) to the point (8, 5) can be calculated using the formula for the slope:
\[ m = \frac{\Delta y}{\Delta x} = \frac{5 - 0}{8 - 0} = \frac{5}{8} \]
Thus, the equation of the line in slope-intercept form \( y = mx + b \) where \( b = 0 \) (since it passes through the origin) is:
\[ y = \frac{5}{8}x \]
Now, looking closely at the provided options, option A can be rewritten from a fraction to match the calculation above:
A. \( y = \frac{5}{8}x \)
Thus, the correct answer is:
A. \( y = \frac{5}{8}x \)