1. The problem states that triangles ABD and ACE are similar right triangles and asks which ratio explains why the slope of AB equals the slope of AC. 2. Recall that the slope of a line segment is the ratio of the vertical change to the horizontal change between two points. For segment AB, slope $m_{AB} = \frac{BD}{DA}$, and for segment AC, slope $m_{AC} = \frac{CE}{EA}$. 3. Since triangles ABD and ACE are similar, corresponding sides are proportional. This means: $$\frac{BD}{DA} = \frac{CE}{EA}$$ 4. This equality of ratios shows that the vertical over horizontal ratios (slopes) of AB and AC are equal. 5. Therefore, the ratio $\frac{BD}{DA} = \frac{CE}{EA}$ best explains why the slope of AB is the same as the slope of AC. Final answer: $\boxed{\frac{BD}{DA} = \frac{CE}{EA}}$