The Prince William County Board of Supervisors yesterday adopted a budget that will result in a 9 percent increase in real estate taxes for home-owners whose properties have been increasing at the average rate.

The new tax rate is $1.40 per $100 of assessed valuation, based on 100 percent of the current assessment. The new rate cannot be directly compared with the old one because they were derived from different formulas. The 1979 rate was $5.25, but it was based on 33 percent of a five-year-old assessment.

An assessment office spokesman said that a homeowner whose property was worth $30,000 at the time of the last assessment -- 1974 -- would have paid $519.75 in taxes last year. Under the new $1.40 rate, the owner's taxes would go up to $567 -- a 9 percent increase -- assuming an average 35 percent inflationary increase since 1974.

Owners whose properties did not appreciate on the average since 1974 will have a smaller increase, and, according to Board Chairman Kathleen K. Seefeldt, some owners might not have any tax increase at all.

Overall, more real estate tax revenue will have to be collected, because the supervisors adopted a general operating budget for fiscal 1981 that was increased 11.4 percent -- from the current year's $114 million to $127 million.

Seefeldt said there were "modest increases" in personnel for police and fire and rescue services.

The supervisors adopted a school budget that rose from $75 million to $90 million, but that amount was $1.375 million less than the school board recommended.