This is simple and wont expand to include anything else or paste to other rows (as per your request)
Sub Copy_It()
If Sheets("Sheet1").Range("A1").Value = Sheets("Sheet2").Range("A1").Value Then
Sheets("Sheet1").Range("A2:" & Range("A1").End(xlToRight).Address).Copy Destination:=Sheets("Sheet2").Range("B1")
Application.CutCopyMode = False
End If
End Sub
However, if you simply add a formula to sheet2 cells from B1 onwards it will simply display the contents of sheet1 if there is a match in the same row
Put this in Sheet2 cell B1 and copy across =IF($A$1=Sheet1!$A$1,Sheet1!B$1,"")