The Procrastinating Against Homework (or anything else excluding reading Brandon) Guild!

[Just-A-Stick she/her]

On 3/6/2026 at 11:46 AM, Throw TheLiving Silverware said:

Yeah this is right up my alley

If a bit far behind

Tell me when and how you prefer to do it

Like this?

Spoiler

idk if i'm doing this right??

[Throw TheLiving Silverware he/him/il/lui]

On 3/8/2026 at 1:26 AM, Just-A-Stick said:

Like this?

  Hide contents

idk if i'm doing this right??

Sorry for taking so long to answer

I was thinking like, how do you prefer the "class" to happen

DMs here or on Discord, voice call, idk

I'll take that you prefer to do it in this thread then 

 

Those results are all correct, you're doing it right. (Idk if your teacher told you, but when you have your equation, you can replace X by the first number of one of the points' coordinates, and if it gives you the second number of the same coordinates, then it's good. Like for the first one, the equation you get is y=-2x+1. One of the points is (1,-1). So we check that -2 * 1 + 1 is equal to -1, which it is. So you did it right)

 

But I feel you're still a bit confused; do you feel you understand what you're doing, what the Xs and Ys are?

[Just-A-Stick she/her]

On 3/10/2026 at 6:35 PM, Throw TheLiving Silverware said:

Sorry for taking so long to answer

I was thinking like, how do you prefer the "class" to happen

DMs here or on Discord, voice call, idk

I'll take that you prefer to do it in this thread then 

 

Those results are all correct, you're doing it right. (Idk if your teacher told you, but when you have your equation, you can replace X by the first number of one of the points' coordinates, and if it gives you the second number of the same coordinates, then it's good. Like for the first one, the equation you get is y=-2x+1. One of the points is (1,-1). So we check that -2 * 1 + 1 is equal to -1, which it is. So you did it right)

 

But I feel you're still a bit confused; do you feel you understand what you're doing, what the Xs and Ys are?

To be honest I feel like I'm bullcrapping my way through all this without actually understanding what I'm doing and how it changes the eqation? Like i know 4+4=8 because i can see it and understand it in my brain. 4+4=8. End of story. But when you throw in complicated stuff my brain stops absorbing information so I don't understand any of it... except the whole "whatever you do to one side of the equation, you also have to do to the other side. the = is the middle line." thing.

[Throw TheLiving Silverware he/him/il/lui]

On 3/12/2026 at 2:43 PM, Just-A-Stick said:

To be honest I feel like I'm bullcrapping my way through all this without actually understanding what I'm doing and how it changes the eqation? Like i know 4+4=8 because i can see it and understand it in my brain. 4+4=8. End of story. But when you throw in complicated stuff my brain stops absorbing information so I don't understand any of it... except the whole "whatever you do to one side of the equation, you also have to do to the other side. the = is the middle line." thing.

Does it help if I try to re-explain the thing to you here? So you'll be able to go through it at your own pace?

(Note: it will probably be slightly different from what your teacher said at some points. That's because I was taught this class with slightly different methods, drawn up by different people. Also, this was 8 years ago and I have forgotten most of the actual class, but I have played around with those elements for years since - but more so in physics and chemistry than math. I apologize in advance for any inconsistency.)

 

The really key thing is that x and y are numbers. Normal numbers, like 4 or -9 or 129.4823 or 10000. You don't know them, but know some things about them. And the equation expresses what you know about them. So you want to rewrite the information in the equation in a way that lets you find the unknowns if possible, and get more information otherwise. (The unknowns are the numbers you don't know, like x and y. Maths has some jargon at times, but don't let that scare you.)

If you only have one unknown, it's easy, because you can always rearrange in a way that tells you the unknown outright. You probably already learned how to do that: add, substract, multiply and divide until you get to something like x=some number. But if you have two unknowns, one single equation is not enough to tell you both unknowns. There are an infinity of possible solutions. For instance, if you know that y=3x+1, then it is true for x=0 and y=1. But it is also true for x=1 and y=4, or for x=74 and y=223, or for x=-5 and y=-14, or for an infinity of other solutions.

But if we take all the possible solutions of the equation, and put them on a graph, look at what we've got: 

A straight line. We have all possible solutions of the equation y=3x+1 right under our eyes. Cool, isn't it? This is what we call: the line of the equation y=3x+1. 

It turns out, any linear equation (that is, an equation of the form y=mx+b, where m and b are any two numbers) has such a line. Hence their name 

 

You will notice something on that graph: this line goes up pretty sharply. In fact, every time we progress by 1 unit horizontally, the line goes up by 3 units.

Wait a minute... 3... like in y=3x+1?

Yeah, that's right: the line of the equation y=mx+b always goes up by m units for every horizontal unit. (And so if m is negative, the line goes down instead.) m determines entirely how fast the line goes. So for that reason, m is called sometimes called the slope.

 

 

But now, we want to do it the other way around: we have some points that are on the line, and we want to find the equation that corresponds to that line. (This is a situation you often end up in physics and beyond, because quite a few situations can be modeled with a linear relation between two variables.) Well, we know that there is only a single line going through two given points. (Geometry theorem you saw a couple years ago, and might even remember.) But how to find it?

Let's properly write everything we have first: we have two points A and B. Their coordinates are (x_A,y_A) and (x_B,y_B). They define a line of equation y=mx+b.

 

Well, we have a formula that can give us m straight up. It is the one you were applying in your sheet: m= (y_B-y_A)/(x_B-x_A). If you're curious and want to see where that formula's coming from, look inside the spoiler tag, but it's not critical. Just understand that this formula gives us the slope, and be able to use it as you are.

 

Spoiler

Remember when I told you that the line went up by m units every 1 horizontal unit? Well, it also means that it goes up by 2m units every 2 horizontal units, by 9m units every 9 horizontal units, by 65.41m units every 65.41 horizontal units... right?

So what if we looked at how much units there are between our two points, and look by how much the slope goes up in that interval?

We have (x_B-x_A) horizontal units between A and B. And between A and B, the line goes up by (y_B-y_A). So the line went up by (y_B-y_A) units vertically in (x_B-x_A) horizontal units. In other words, (y_B-y_A) = (x_B-x_A)m. Which can also be written as m= (y_B-y_A)/(x_B-x_A).

Now we've got a formula, let's get back to what we were doing.

Then, we still need to find b. But, our two buddies the points A and B are on the line. So their coords are both valid solutions for the equation, meaning that, for instance, y_A=mx_A +b. Replace , m, and  by their number values, and you now have an equation with one unknown. Taking the first point from your first exercise, it would be like 7 = -2*-3 +b.

Would you look at that? There is only one thing we don't know in that equation, and it's b! It's only a matter of moving the numbers around until we arrive at b=some number. Here:

7 = 6 + b

7-6 = b

1 = b

b=1

And. Here. We. Are. We got both of the coefficients we wanted, m and b, which means we have our linear equation fully sorted. And all that from two points. Pretty cool, isn't it?

 

If there's anything I said that wasn't clear, please ask. I'll do my best to make it more understandable 

[Just-A-Stick she/her]

1 hour ago, Throw TheLiving Silverware said:

Does it help if I try to re-explain the thing to you here? So you'll be able to go through it at your own pace?

(Note: it will probably be slightly different from what your teacher said at some points. That's because I was taught this class with slightly different methods, drawn up by different people. Also, this was 8 years ago and I have forgotten most of the actual class, but I have played around with those elements for years since - but more so in physics and chemistry than math. I apologize in advance for any inconsistency.)

 

The really key thing is that x and y are numbers. Normal numbers, like 4 or -9 or 129.4823 or 10000. You don't know them, but know some things about them. And the equation expresses what you know about them. So you want to rewrite the information in the equation in a way that lets you find the unknowns if possible, and get more information otherwise. (The unknowns are the numbers you don't know, like x and y. Maths has some jargon at times, but don't let that scare you.)

If you only have one unknown, it's easy, because you can always rearrange in a way that tells you the unknown outright. You probably already learned how to do that: add, substract, multiply and divide until you get to something like x=some number. But if you have two unknowns, one single equation is not enough to tell you both unknowns. There are an infinity of possible solutions. For instance, if you know that y=3x+1, then it is true for x=0 and y=1. But it is also true for x=1 and y=4, or for x=74 and y=223, or for x=-5 and y=-14, or for an infinity of other solutions.

But if we take all the possible solutions of the equation, and put them on a graph, look at what we've got: 

A straight line. We have all possible solutions of the equation y=3x+1 right under our eyes. Cool, isn't it? This is what we call: the line of the equation y=3x+1. 

It turns out, any linear equation (that is, an equation of the form y=mx+b, where m and b are any two numbers) has such a line. Hence their name 

 

You will notice something on that graph: this line goes up pretty sharply. In fact, every time we progress by 1 unit horizontally, the line goes up by 3 units.

Wait a minute... 3... like in y=3x+1?

Yeah, that's right: the line of the equation y=mx+b always goes up by m units for every horizontal unit. (And so if m is negative, the line goes down instead.) m determines entirely how fast the line goes. So for that reason, m is called sometimes called the slope.

 

 

But now, we want to do it the other way around: we have some points that are on the line, and we want to find the equation that corresponds to that line. (This is a situation you often end up in physics and beyond, because quite a few situations can be modeled with a linear relation between two variables.) Well, we know that there is only a single line going through two given points. (Geometry theorem you saw a couple years ago, and might even remember.) But how to find it?

Let's properly write everything we have first: we have two points A and B. Their coordinates are (x_A,y_A) and (x_B,y_B). They define a line of equation y=mx+b.

 

Well, we have a formula that can give us m straight up. It is the one you were applying in your sheet: m= (y_B-y_A)/(x_B-x_A). If you're curious and want to see where that formula's coming from, look inside the spoiler tag, but it's not critical. Just understand that this formula gives us the slope, and be able to use it as you are.

 

  Reveal hidden contents

Remember when I told you that the line went up by m units every 1 horizontal unit? Well, it also means that it goes up by 2m units every 2 horizontal units, by 9m units every 9 horizontal units, by 65.41m units every 65.41 horizontal units... right?

So what if we looked at how much units there are between our two points, and look by how much the slope goes up in that interval?

We have (x_B-x_A) horizontal units between A and B. And between A and B, the line goes up by (y_B-y_A). So the line went up by (y_B-y_A) units vertically in (x_B-x_A) horizontal units. In other words, (y_B-y_A) = (x_B-x_A)m. Which can also be written as m= (y_B-y_A)/(x_B-x_A).

Now we've got a formula, let's get back to what we were doing.

Then, we still need to find b. But, our two buddies the points A and B are on the line. So their coords are both valid solutions for the equation, meaning that, for instance, y_A=mx_A +b. Replace , m, and  by their number values, and you now have an equation with one unknown. Taking the first point from your first exercise, it would be like 7 = -2*-3 +b.

Would you look at that? There is only one thing we don't know in that equation, and it's b! It's only a matter of moving the numbers around until we arrive at b=some number. Here:

7 = 6 + b

7-6 = b

1 = b

b=1

And. Here. We. Are. We got both of the coefficients we wanted, m and b, which means we have our linear equation fully sorted. And all that from two points. Pretty cool, isn't it?

 

If there's anything I said that wasn't clear, please ask. I'll do my best to make it more understandable 

legitimately, that makes so much more sense. Thank you so much!!!

I'll try it this upcoming week and PM you if I end up with any confusion/questions  

[Throw TheLiving Silverware he/him/il/lui]

10 hours ago, Just-A-Stick said:

legitimately, that makes so much more sense. Thank you so much!!!

I'll try it this upcoming week and PM you if I end up with any confusion/questions  

Glad to hear that sis 

Spoiler

No, really, I was so afraid that there would be something I didn't explain or got over too quick because I took it for granted or sthg

I'm happy I was able to help

 

[NerdSandwich she/her]

Hey I like this thread

Boo homework

Ngl I don't have much but still

[KaladinsSenseOfHumourSpren He/Him]

YES!

This is me

80% of the time I'm on the Shard, I'm procrastinating

[NerdSandwich she/her]

I'm always procrastinating-I just might not know it yet.

[Just-A-Stick she/her]

@Throw TheLiving Silverware

i did maths for 3.5 hours straight today catching up on things and i kind of (ish) understand it a little bit thanks to you and google ai

thank youuuuu