It is not a smorgasboard. Your facts and circumstances decide which you must do. Based on yours:
Pretend you got a 1099-MISC for that income. File Schedule C.
And you report it exactly the same as if you had gotten a 1099-MISC. This means you must go through the rigmarole of filing Schedule C, which will seem weird because you don't have a sole proprietorship. Actually, you do. You become a "sole proprietorship" (or "partnership") by default, anytime you do business without a more formal structure like an LLC or corporation.
Documentation of this area used to be quite poor, but the emerging gig economy has led IRS to create a site just for that.
Also file Schedule SE.
I tried to classify this as line 1 employee income; can't do it. The barrier is SS/Medicare/SE tax. For the same reason, reporting this on Schedule 1 Line 8 is flat wrong for you. By using Schedule C, the number drops right into the easy short-form Schedule SE, and you're done... and that saves you the eye-burn of even trying to read the long-form Schedule SE.
You need to file Schedule SE because you are just above the reporting threshold for it. If you had made < $433 (really) *, you wouldn't need to file Form SE. You might want to find some business expenses e.g. travel (transit, or IRS's mileage rules), or double-check your numbers.
Paying SE tax isn't all bad. When you retire, your social security benefit is decided by how much money you made while working. This posts as income for that purpose.
From Pub. 525 (IRS's deep-dive guide into what income is):
Generally, if you work in the gig economy or did gig work, you must include all income received from all jobs... See the Instructions for Schedule C (Form 1040 or 1040-SR) and the Instructions for Schedule SE (Form 1040 or 1040-SR).
From Sched. C instructions:
Use Schedule C (Form 1040 or 1040-SR) to report income or (loss) from a business you operated or a profession you practiced as a sole proprietor. An activity qualifies as a business if your primary purpose for engaging in the activity is for income or profit and you are involved in the activity with continuity and regularity.
The only "out" Schedule C gives you is if the activity is "sporadic", then it may not qualify as a business and could be reported on Sched 1 Line 8. But I doubt that applies since you are presumably open to more tutoring business if you can get it. Even if you could argue that, and get that argument to stand up in an audit, I still wouldn't bother -- you still have to deal with Schedule SE; and the Schedule C path is the easier way to do that.
The only other out is "hobby". I hang out with hobbyists who regularly try to "game" the difference between hobby and business, either to deduct hobby expenses or evade SE tax on work. That trick never works. IRS is wise to it, and will quickly refuse you, alter your return, notify you of penalties and interest, and say "if you disagree, sue us. Here's how."
My friends make the mistake of wrapping themselves up in self-justification. But the fact is, IRS uses the plain-English version of "hobby". From the IRS Small Business FAQ:
A hobby activity is done mainly for recreation or pleasure.
What matters is how a cool outsider sees it. Its it a hobby or business for most people who do it? Is the lion's share of your activity conducted in a hobby manner (i.e. as a passion project)? Sometimes (not here), that's a tough noodle to stick to the wall, and that link has more documentation to help you determine; but never forget the core definition above.
- Here's a dog that won't hunt: "Tutoring is a lifelong avocation that I only do when I'm paid".
You will not deal with anyone willing to listen to your argument until you sue IRS. Having done this and won, I can tell you it's a waste of time unless you have a strong understanding of Tax code and can coherently argue the law (and present provable facts). I would not want to argue tutoring as hobby.
Given that tutoring for pay is a classic student job... and OP, you give no evidence of tutoring as a passion project... I see any "hobby" claim as undefendable. Hence I don't advise it, and have excluded it from my advice. It might work for other readers if their facts support it, but don't fool yourself.
* Really. $433 not $400. Punch $432 into Schedule SE and see what happens.