Some carpet cleaning pastor shown in the table the relationship is linear find interpret the rate of change in the initial value for the situation the table is rooms cleaned over cost on rooms cleaned is 1234 and on cost is 125 175 to 225 275

It would help so much if you were to type out the table in table format.  What does "1234" stand for, and where do you find it in the table?  I urge you to copy the original problem here, all of it.  Or, could you take a photo or screen shot of the original problem and then share the illustration here?

Is this what you meant?  Probably yes, but I wish I didn't have to guess.

Rooms
cleaned      Cost
  1                $125
  2                $175
  3                 $225
  4                 $275

You can see for yourself that the increase from $125 to $175 is $50.  From $175 to $225 the increase is the same ($50).  And so on.

So, after the first room has been cleaned, the cost of having additional rooms cleaned is $50 per room.

Just to get the cleaner to your house apparently costs $75.

Then $75 + 1($50) = $125 for one room.

The mode of the numbers is 29.