If you want to understand how Congress shot down Nelson Brooke's hopes for a summer vacation, you need only take a look at line 15 of Internal Revenue Service Form 219.

That's where taxpayers report how much of the profit from selling their homes can be excluded from taxation. In the huge tax bill passed in final form yesterday. Congress decreed that the maximum tax-free profit for taxpayers 55 or older who haven't used the exclusion before will increase from the present $100,000 to $125,000 -- if the house was sold after July 20, 1981.

Nelson Brooke's job is to explain all that within the confines of a single line (about 14 words) of the tax form.

And that's just one of a thousand such tasks immediately facing Brooke, a spirited, 38-year-old member of the Senior Executive Service who is chairman of the IRS's Tax Forms Coordinating Committee -- and the agency's Frank Lloyd Wright of forms.

Brooke and the 25 accountants, lawyers and editors on his forms development staff will be working furiously in the next six weeks, revising old forms and devising new ones to incorporate congressional tax decisions. The job must be finished by mid-September to leave enough time for printing the hundreds of millions of copies of IRS forms that the nation consumes each tax season.

In a way, this is all standard operating procedure for the federal government. Congress writes the law, of course, but the executive agencies write the voluminous regulations and paperwork necessary to make the law work.

Usually, though, it is not such a rush job. for most laws as sweeping as the new tax bill, the process of producing regulations, instructions, tables and forms would take a year or more. For that matter, some of the big changes in the new tax bill, including relief from the "marriage penalty" and the relaxed rules on charitable deductions, won't take effect until 1982, meaning Brooke and his form writers can put them off for the moment.

But there is still a huge amount of work to be done right away. And the need for speed is heightened because this year, for the first time, the new Paperwork Act dictates that every form Brooke designs has to be approved by the Office of Management and Budget before it can be printed.

Brooke talks about his forms with the afternoon of an artist recalling a favorite painting. "You take that 990," he said of the return tax-exempt organizations must file. "That's not widely known, but it's a good form."

Brooke learned the importance of simple, intelligible forms during his years as a field auditor for the IRS.

"A few people are going to read the law, and some specialists will know about the obscure rulings," he said, "but Form 1040 is the way we talk to the public."

The problem is that many sections of the law Congress just passed will make the Tax Code, and the forms based on it, even more complicated than they are now.

The revised capital gains provisions will require the addition of an eighth column to Schedule D, a document that even accountants find formidable in its current seven-column manifestation. The new "accelerated cost recovery" system requires such labyrinthine calculations that a new form, 4562A, probably will have to be appended to the standard depreciation form. The new tax break for certain adoption expenses is so confusing that Brooke can't figure out what section of Form 1040 it belongs in.

Which raises a new problem: 1040 overload. The basic tax form is already jammed with type from margin to margin. The new law will permit Brooke to eliminate three exising lines, but it adds requirements for five new ones. "It's tight, real tight," Brooke said yesterday when he counted that up. "But we'll squeeze it all in. We have to -- it's the law." CAPTION:

Picture, Nelson Brooke faces a few weeks' work: revising tax forms to incorporate new law. By Doug Menuez -- The Washington Post