r/askmath • u/DickVanJumpstyle • Oct 12 '20
Need some arbitration. Linear equation. Argument in comments.
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u/miketinn Oct 12 '20
This is the function of a straight line. It is an introduction into functions which can get far more complex and useful and are used to model many relevant aspects of life. Why are children taught them? So that those children that do want to proceed in science and engineering fields can discover their ability.
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u/Jackm941 Oct 13 '20
Hate when people say no one uses this stuff, im only starting my engineering path well in my 3rd uear of uni and so far using functions for things like suspension seems really intresting for me as im into motocross and cars etc so damping and rebound etc is cool to see in math form. Vibration stuff to is cool to me. And no im doing electronics and i dont get it but its easy to see how needing to know complex functions is important for radio communications etc.
People really think all this stuff is just magic and you dont need to know math for it or what?
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u/miketinn Oct 13 '20
Good luck with your studies! It's concerning we live in times where people think knowledge and rediscovering for ourselves what the great minds before us have found is pointless, because if you want to know something you can google it. Those sad arguments as to why they still teach maths because everything is done on devices anyway? We are effectively finding ourselves in a situation where we have an increasingly dumbed down population that is easily manipulated and can't distinguish for themselves fact from fiction.
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u/shewel_item Oct 13 '20
Answer to Angelina Elizabeth: so you can start taking derivatives (at any point on any given line), so you can start tracking the growth of your own stock portfolio. And, no -- no one talks about it that much, because they want you to focus on your studies, ofc.
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u/quijanas Oct 12 '20
The major issue with this problem is that you won't ever get more than two drinks IF YOU DON'T tip on the first two!
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Oct 12 '20 edited Oct 12 '20
I would use an inequality to solve this e.g. 10+5x≤50
I think the worded problem was a bad example.
Here's one:
A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly and at a constant rate. After 8 months, he weighed 138 kilograms. He started at 90 kilograms. Let y represent the sumo wrestler's weight (in kilograms) after x months. Complete the equation:
From that worded problem we can gather the following two points. 0,90 8,138
Now that we have 2 points we can solve the gradient which is 6.
So the equation is Y=6x+90.
As for op's Facebook screen shot, I'd argue it's more or less graphs are just important and y=mx+b is kind of the quadratic equation for graphs, not the best analogy but you get what I mean.
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Oct 13 '20
You can settle this by assigning units to each part of the equation y = mx + b
y = 50 dollars
m = 5 dollars per 1 drink
x = 8 drinks
b = 10 dollars
A slope has two units, and the only piece of the equation that has two units is m
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Oct 13 '20 edited Oct 13 '20
Side note.. if you want to find the slope of a line, pick any two points on the line.
Slope = (y1 - y0) / (x1 - x0)
We already know 8 drinks is $50. So let’s use that as one point. (x0, y0) = (8 drinks, $50)
10 drinks will end up being $60, so (x1, y1) = (10 drinks, $60)
($60 - $50) / (10 drinks - 8 drinks) = $10 / 2 drinks = $5 per drink = m
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u/Uli_Minati Desmos 😚 Oct 13 '20
Good practice to solving text problems with functions:
- Which quantity is variable and its value can be (almost) anything? x
- Which quantity is variable, but its value depends on x? y
- What value does y have when x is zero? b
- When you increase x by 1, how much does y increase? m
- If you can't answer 3. or 4.: Do you know any values of y which correspond to a value of x? Plug it into y=mx+b
Unusual but correct version:
- You pay different amounts of money, so x: money paid in $
- You receive different amounts of drinks depending on how much you paid, so y: number of drinks
- When you pay zero, it's not quite clear how many drinks you get since you wouldn't get into the club. Skip this one for now. (Also called "solving for b")
- When you pay +1$, you would (mathematically) only get a fifth of a drink. m=1/5
- We know that zero drinks cost 10$. This gives us 0 = 1/5*10+b => b=-2
- Now we can plug 50$ into the equation! y = 1/5*50-2 = 8
The usual version:
- You buy different amounts of drinks, so x: number of drinks
- You pay different amounts of money depending on how many drinks you bought, so y: money paid in $
- When you buy zero, you pay 10$.
- When you buy +1 drink, you pay another 5$.
- We know everything!
- Now we can plug 50$ into the equation! 50 = 5*x+10 => x=8
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u/Reap_sin Oct 13 '20
So, there's a lot of things going on here, that have gone unsaid.
First and foremost: we had always agreed that the standard for y=mx+b is that m is the slope. But I posited that commutative property allowed for a potential slip in the picture as calling the number of drinks (left to be vaiable x) the slope.
Understanding the standard function and nomenclature, I was trying to help my buddy here understand that variables become what you assign them. Meaning; if you replace the variables in y=mx+b to any other variation of letters, and remove the context of identifying the standard definitions of the variables, the equation still works for the intended purpose.
Also, starting that (y=mx+b) = (y=xm+b) as an example of how the written [number of drinks = slope] is possible, even though it would visually change the graph, which is unimportant to the context of the original content.
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u/Genshed Oct 19 '20
Not being a mathematician, my first reaction to this question was - who doesn't tip the bartender in a club?!
That's a variable that is not determined by the terms of the problem.
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u/yaakovb39 Nov 02 '20
x = 8, how is this a slope?
Replace 50$ with Y and you get an actual linear equation
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u/DickVanJumpstyle Oct 12 '20
My friend and I are having a disagreement about this. I said that in this case X would not be the slope, but that $5 is the slope and that $50 and how many drinks that buys at this bar are variables. u/Reap_sin argues that $50 is constant and the only variable is X, which can be the slope because of the commutative property. That if you plug in the given values it would all come out the same, i.e. if b is 10 and y is $50 then if the slope is 8 then x is 5 and if the slope is 5 then x is 8.