The other tutor did it correctly but by a slightly different method and
also it needs to be placed in the form Ax + By = C, not the form he left
it in.

Use the slope formula: , , , 









Use the point-slope formula:



y - 1 = 1(x-4)

y - 1 = x - 4

y - x = -3

Swap the terms on the left to get x first because Ax+By=C has x first

-x + y = -3

Make the coefficient of x positive by multiplying every
term by -1 which changes the sign of ever term on both sides:

x - y = 3

That's the answer in Ax + By = C form 

where A=1,  B = -1, and C = 3

You could write it this way

1x + (-1)y = 3

to show both the A and the B, but probably you just want

x - y = 3

Edwin