Although you said linear, I assume you really can live with a staircase.
If that's the case, and I understand the question correctly, then it's just simple math.

Your example: ramp from 10 (x) to 560 (y) in 42 seconds (n).
Suppose you want 1 step per second. In that case:
stepsize = (y-x)/n
output = x
FOR QQ = 1 to n
PAUSE 1000
output = x + stepsize
next QQ
Replace the pause with a 1 second interrupt if you need to do other things.
"output" feeds yout DAC