College Algebra - Linear Equations
Let me start with some basics, and if this is too basic, just let me know.
So - the philosohy of linear equations. What is their raison d'etre, and why are you being made to learn them?
Think about it like this.
There is some relationship that exists in nature (or in life, if you prefer) between things you know (or can control), and things you'd like to know that depend on those 'controllable' things.
You want to get a hold of that 'relationship' and make it work for you - so you can describe and predict stuff 'in life' that follows that relationship.
That's what math can do for us!!
All that notation - the x's the y's, the operators - and all that graphing, is supposed to make it easier! And it does. But only if you speak the language and understand how to translate:
What you want to know to help you in life
to
Mathematical symbology
I am going to try to make this clear with an example and maybe we can work through some questions you have, or problems you're working on.
Example to follow in a few...sound good?
@CaloenasNicobarica
@BurningEmber The same stuff? Cool! Is this thread helping at all? Do you have any questions? If so, post 'em and we'll keep this going! 
@BurningEmber Awesome. I am ready to talk math any time!
@CaloenasNicobarica Something I'd like to point out about the previous example. Notice that I illustrated the exact same relationship between (number of hours of tutoring) and (total earned) in 3 different ways.
1. In words.
2. As a linear equation.
3. Graphically.
The idea here is that, from 1 -> 3, it should get easier for you to tell me the 'output' of the relationship (total $) given the 'input' (hours).
I'm kind of trying to get across the motivation for the symbols and graphs and the connections between those and what you really, actually want to know.
How badly am I failing to do so? 
I'm new at tutoring this way.
@BurkeDevlin
@BurkeDevlin
You're not failing at anything. I like your dorky graphy chartboo! So 5 hours = coffee. *exchanges out tea for a pot of coffee instead*
But seriously. I do see the correlation. And once you plug in the numbers it works as a machine. I mean- in programming this is basically what's happening. I can do equations like this, and I can see the graphical correlation... Hnn... There's this one mechanisms that appear to be the same that I'm struggling with. Oh wait... now that I'm looking at it...it actually makes sense. O___O; So the x is variable, and then y adjusts and those are also your coordinates. I see.
Alright. So... I have some example problems that I kinda wanna see worked out. For some reason it feels like I'm missing something- but I'm pretty sure it's the same procedure!
x-2y = 15
Determine the missing coordinate pair in the ordered pair (-1, ?) so that it will satisfy the given equation.
Oh, I can join you in there in a sec. TY.
@CaloenasNicobarica
Graphing fractions - here is an ordered pair (1/4, 3/2). I've expanded the scale a little to show that there is a lot of room between the 0 and 1, and between the 1 and 2. Each axis is an entire continuum, not just a discrete set of whole numbers. Usually only the whole numbers are labeled, but any fractional number can fit in between.
