WTF is slope?

[supa]

So I'm in one of those unfortunate circumstances of being a dad trying to help his son with math but have never taken any upper level math classes. I'm pretty good at figuring a lot of stuff out if I understand what we're trying to accomplish, but I need something tangible to go by.

Basically I'm just trying to figure out what slope refers to in a math equation. Is it just the fact that when you put coordinates on a graph it creates a sloped line?

What the hell does m represent?

I can copy/paste the actual problem we're working on but I'm more looking for a way to understand it, not the actual answer.

[boost]

slope is x/y. It is simply a way to measure how steep a given line is relative to x and y. For example, a 45° line would give you a slop of 1, because at any point in the line you could draw a line parallel to the x axis, then draw one from the end of that line parallel to the y axis until it intersects with the line again and these two legs would be equal, giving you 1/1 or 1. As the line gets steeper, the y variable increases, and as it becomes more horizontal the x variable increases.

I have completely forgot what m represents.

Hope this hasn't been too basic... finding the slope of a point (each point on a curved line has a particular slope, the line itself does not have one) on a curved line is a bit more tricky. I could explain how to do it conceptually, but I can't remember what equations to use and where to plug what in to figure out what the slope of a given curved line is.

[lolzzz_321]

slope is y/x u nub

isn't m the same thing as slope I remember some y=m(x) + b shiz

[lolzzz_321]

you should post a problem and someone will give you a comprehensive answer

[boost]

oh fuck.. I always reverse it on accident

it is indeed y/x


edit: isn't m just another way of saying slope? like y/x = m

But m is written as a integer or as a decimal. for example, a line with a slope of 5/2 would be said to have an m of 2.5

edit2: lol it is sad that I am unsure of such basic maths...

[kiwiMark]

We say gradient in fancy countries. And yeah we also use m as in y = mx + c for the equation of a line.

[a500lbgorilla]

We say gradient in fancy countries. And yeah we also use m as in y = mx + c for the equation of a line.

lol c, learn math in a beddar country.

[boost]

what does c represent?

[lolzzz_321]

constant

[kiwiMark]

c is the Y-intercept, or where the line crosses the Y axis.

So if you have the equation y = 1x (ie. m = 1) then you have a line that starts at 0 and for every one unit that you go across the line also goes up one unit. If you have the equation y = 1x + 5, then your line looks exactly the same but has been moved five units up (easy to see if you draw it or just plug in some x and y values)

[boost]

ah, yes

[a500lbgorilla]

So I'm in one of those unfortunate circumstances of being a dad trying to help his son with math but have never taken any upper level math classes. I'm pretty good at figuring a lot of stuff out if I understand what we're trying to accomplish, but I need something tangible to go by.

Basically I'm just trying to figure out what slope refers to in a math equation. Is it just the fact that when you put coordinates on a graph it creates a sloped line?

What the hell does m represent?

I can copy/paste the actual problem we're working on but I'm more looking for a way to understand it, not the actual answer.

It's rise over run.



The line is defined by an equation y=mx+b

The equation just says that for all x values, this will be your y-value. Then you pick any old x-value, and it will yield you a y.

So for an x value of 0, you will have y = b where b is the y-intercept.

For x = 1, y = (rise/run)*1 + y-intercept

Slope speaks of the rate of change of the value of y with respect to x. So if your slope is m=2, then for every change in x of +1, there will be a change in y of +2.

[rong]

Wait, what? The c in y=mx+c isn't universal?

[a500lbgorilla]

Wait, what? The c in y=mx+c isn't universal?

+c is for integrals.

inb4 antiderivatives.

[BooG690]

I never knew FTR was so fail at maths.

[Roid_Rage]

This thread has provided me with many laughs.

[BennyLaRue]

What the hell does m represent?

Don't overthink it. It's low. Just shove.

[!Luck]

Algebra: Slope | Core Algebra | Khan Academy

[bigred]

What is M in a slippery slope?

[bigred]

I'm for derivatives!

[supa]

JKDS gave me a crash course on the subject. The actual issue was we were working with word problems and I needed to understand how y/x related to the question. Renaming y and x as (in this case) product and dollars made it make sense.

Thanks again J!

[kingnat]

For once I will give non-America props... it would be so awesome if we used "gradient" instead of slope. Slope is how a value changes with respect to another. In all the cases above, it's how "y" changes with respect to "x". For linear functions that rate of change is constant, hence it follows the form of y = mx + b. At any one value of "x" you can determine the slope by drawing a line tangent to the "curve". Again for linear functions this is always just a constnat, and is always the same.

Calculus drops the "linear only" premise, and gives you tools to calculating the slope (i.e. how one variable changes with respect to another) for a load of different functions. In the physics, you often want to determine how something changes with respect to all 3-dimensional space... and it's only at this point that US kids call this "gradient". It's labeled as an upside down delta.

[bigred]

@kingnat

[givememyleg]

y=mx+b for life!

[Sasquach991]

If the slope of a horizontal line is 0,
what is the slope of a vertical line?

What is 1 - i 2 ? It didn't accept the font. What is 1 minus i squared?

And the Y intercept is (0,b) not b

[supa]

If the slope of a horizontal line is 0,
what is the slope of a vertical line? My instinct would be to say 90, but I don't think that makes sense, seeing how a slope of 1 would be 45 degrees, I think.

What is 1 - i 2 ? It didn't accept the font. What is 1 minus i squared? -1sasquatch?

And the Y intercept is (0,b) not b

I thought the 0 was implied?

[a500lbgorilla]

A horizontal line would be y = 5. m = 0.

A vertical line would be x = 5. m has no meaning.

edit and i^2 is -1. It's more interesting to ask what is 1-sqrt(-1) but only barely.

Edit I take that back, imaginary numbers and the complex plane are cool.

[Sasquach991]

A horizontal line would be y = 5. m = 0.

A vertical line would be x = 5. m has no meaning.

edit and i^2 is -1. It's more interesting to ask what is 1-sqrt(-1) but only barely.

Edit I take that back, imaginary numbers and the complex plane are cool.

I forgot about the ^ character.

I agree. Complex numbers are cool.

Why do electrical engineers use "j" instead of "i" for imaginary numbers?

Not sure what the Brits use.

/geek

[supa]

A horizontal line would be y = 5. m = 0.

A vertical line would be x = 5. m has no meaning.

This makes no sense to me. I understand why m = 0 on a horizontal line and why it has no meaning on a vertical line. But why are y and x 5? Or is that just an arbitrary number you pulled out of your butt?

[Illfavor]

y = whatever the y intercept of the horizontal line is, x as well.

[kickass]

i thought "slope" was a racial slur for the vietnamese folkses. Im pretty sure clint says it in gran torino. learn somthing new everyday.

[Sasquach991]

As the slope increases, y increases and x decreases where Y approached infinity and x approaches 0 so you have infinity/zero

Clint would have major trouble with slopes approaching infinity

[kiwiMark]

@supa, yeah the 5's were examples. Y=5 would be a flat line where every point on the line is 5 units high (ie. 5 on the y axis).

The equation of a line is there to describe the relationship between two variables (x and y), so you can say hey if I plug in the value 10 for X, what does y come out to be? (eg. for the line y = 1x + 0, we'd have the equation y = 1*10 + 0 so y is 10 when x is 10 on a line with a slope/gradient(m) of 1).
If we're trying to describe a flat line then the Y value remains the same for all values of x (even if x = 3959823 the line is still gonna be 5 units high on the y axis, I mean it's just a flat line sitting there at 5), so we just stop talking about x and say, in this example, Y = 5, as this is always true. A line going straight up and down just needs to be X = 5 (or X = 0, or X = 17, or X = -45, just changes how far left/right we find this vertical line), for the same reason: the X value stays the same no matter what the Y value is doing, so we don't put it in the equation.

iunno if that makes sense or helps

[bode]

f#@$ing math...how does it work?

FYP