How many lines are needed to connect all smiling toasters in a 4x4 grid?

Question

The puzzle is as follows:

How many straight lines do you need to draw the least possible to join
all the smiling toasters if you should not raise the pen or go over
any line already drawn? Remember that it is allowed to cross.

The alternatives given are as follows:

6
5
7
4

How should this puzzle be approached? I'm getting 7 lines, however, I think there are different ways. Is there a way to minimize the trials?
I found this riddle in a book Logical Challenges from 2000's. It seems to be an adaptation from a reprinted copy of Martin Gardner's Puzzle's book from 1970s.
Because this puzzle has a drawing it would help if answers also included drawings so I could properly visualize the lines and understand why they are there.

Glorfindel · Accepted Answer

Here is a solution with six lines:

It's difficult to tell how I found this, except that I already knew a solution for a 3 by 3 grid with 4 lines, which can be found e.g. here on our sister site Mathematics Stack Exchange. It's also possible that a solution with 5 lines exists.
(By the way, the puzzle is missing the requirement that the lines must be orthogonal or diagonal. Otherwise you can simply do something like this, if you extend the lines far enough upwards and downwards.)

Jay · Answer

I don't know if this satisfies the intended problem but it follows the rules. I approached it by looking at the minimum multiple choice answer, and trying to exclude solutions of that size.

How many lines are needed to connect all smiling toasters in a 4x4 grid?

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