Math, or at least this part of it, is all about relationships between values. Let’s ignore numbers for a bit. If you take a long stick and put a big rock under it, then when you move your side of the stick down, the other side will move up. And if you were to measure how much you moved your side versus how much the other side moved, you’d notice that unless you put the rock right in the dead middle, the other side would move a different amount. This isn’t because something is magically making this happen, it just a property of the construction of your system. The other side just does move more or less, and it’s different depending on where the pivot point is.

Similarly, if you have two gear wheels with different numbers of teeth, and you mesh them together, and you turn one and count how many times you’ve turned it, and also count how far the other one has turned, you’ll find a relationship there too! And again, this relationship is just built into the way these objects interact. It’s just the way this system works.

Okay, so, stay with me now, saying y = 2x + 5 is the same. It’s defining a relationship, it’s building a system that’s says the value we’re calling “y”, chosen arbitrarily it could be any name, is always twice as big as “x” (also chosen arbitrarily), and then 5 more than that. It’s a system we’ve built, just like the levers or gears, that produces a relationship we want to express for some reason. And you can put them together in any way, and they’ll always describe some relationship, even if it’s not a useful one.

Now, people have spent hundreds of years, depending on how you want to count, trying to find relationships that also happen to have predictive power. They’ve built systems where the relationship between “d” and “t” is modeled to be the same as the relationship between “the distance that rock flew from me” and “the time since I threw that rock”. And what’s nice about finding these relationships is that now that you know what the relationship is, now that you’ve built the system of levers and pulleys and gears that turn in just the right way, you can start guessing about the rocks before you even throw them, because this relationship you’ve got on the page is similar to the one you’ve seen in real life with the rock and the stopwatch.

Once you’ve got a bunch of these, picking the right one and combining them because more like a puzzle or a maze. I’ve got these things I know, like the weight of the rock, and the size of the Earth, and how stiff the metal in the spring I’m using to launch this thing is. And I’m trying to figure out its top speed. And I’ve got a bag of relationships I know are battle-tested. So all I have to do now is start finding relationships that depend on stuff I know to get me stuff I don’t know. And if I can link them together like a Rube Goldberg machine, I can figure out something I didn’t know using this one relationship, which is handy because this other relationship I’d quite like to use needed that thing I didn’t know before but do now.

And so I can work through a chain of relating things to things until I can get to the point where I have enough to use one of the relationships I do know that predicts speed. And once I’ve got that, I’m done! I trust the relationships I’ve used, presumably I used them properly and didn’t make any dumb mistakes, and so I followed a chain of things I knew, through tools that used those things, to tools that used the things the other tools produced, until I found a path to my goal.

The only thing stopping you from there is the complexity of the relationship, the accuracy of the relationship to the real situation, and how accurately you can measure the things you know.