[python] Search a text file and print related lines in Python?

How do I search a text file for a key-phrase or keyword and then print the line that key-phrase or keyword is in?

with open('file.txt', 'r') as searchfile:
    for line in searchfile:
        if 'searchphrase' in line:
            print line

With apologies to senderle who I blatantly copied.

Note the potential for an out-of-range index with "i+3". You could do something like:

with open("file.txt", "r") as f:
    searchlines = f.readlines()
j=len(searchlines)-1
for i, line in enumerate(searchlines):
    if "searchphrase" in line: 
        k=min(i+3,j)
        for l in searchlines[i:k]: print l,
        print

Edit: maybe not necessary. I just tested some examples. x[y] will give errors if y is out of range, but x[y:z] doesn't seem to give errors for out of range values of y and z.