Final answer:
The translation rule that maps the point (1, 3) to (2, 6) is described by the function T(x, y) = (x + 1, y + 3), which represents a 1 unit rightward and 3 units upward shift.
Step-by-step explanation:
The question is asking for the rule that describes a translation T which moves a point in the coordinate plane from one location to another. In this specific case, the translation T maps the point (1, 3) to (2, 6). A translation can be described by how far the point moves along the x-axis (horizontal shift) and the y-axis (vertical shift).
To find the translation rule, we calculate the difference in the x-coordinates and the y-coordinates of the two points. For the x-coordinates: 2 - 1 = 1 and for the y-coordinates: 6 - 3 = 3. Thus, the point has been translated 1 unit to the right and 3 units up.
The rule that describes this translation is:
T(x, y) = (x + 1, y + 3).