Selecting a range with relative reference

Newbie quesiton, I know.

A cell has been selected in VBA by using "

ActiveCell.Offset(-1, 3).Select

". How do you select a range starting with that point going out to the end of the sheet in the same row?

For example the "

ActiveCell.Offset(-1, 3).Select

" may end up at J3. I want to then select range J3 through IV3.

The start point will be different every time.

Thanks