A line can be uniquely identified by any two points that it passes through. The equation of a line passing through the points `(x_1, y_1)` and `(x_2, y_2)` is given by `(y - y_2)/(x - x_2) = (y_1 - y_2)/(x_1 - x_2)` .

Substituting the coordinates of the points that are given:

`(y - 4)/(x - 1) = (5 - 4)/(8 - 1)`

=> `(y - 4)/(x - 1) = 1/7`

=> `7*(y - 4) = 1*(x - 1)`

=> 7y - 28 = x - 1

=> x - 7y + 27 = 0

**The equation of the line passing through (1, 4) and (8, 5) is x - 7y + 27 = 0**