P48, Coordinate Geometry 6
"Find the equation of a line passing through the points A (5,4) and B (2,3)"
using Y = MX + C (was always taught to use c and not b... sue me

)
As change in y is 1, and change in x is 3, that gives a line of gradient 1/3.
Putting this into the equation and solving where x = 5 and y = 4...
4 = 5/3 + c ... therefore c = 7/3
testing in B where x = 2 and y = 3
3 = 2/3 + 7/3 (correct)
Solution therefore y = x/3 + 7/3

<< since posting I noticed that the solution offered actually uses 6,3 as point B and not 2,3 as in the question