# Learning about finding the slope of a line

1. Mar 18, 2003

### RuroumiKenshin

I just don't get it!

We're learning about finding the slope of a line. And I don't get any of it, so can someone explain it to me? I could find the slope through a pair of points:

C->1(2,1) 1-1 =0
D->2(3,1) 2-3 =-1 and the answer is 0...(note that this is algebra((or pre-algebra)), not calculus)

but when it comes to the graph, I'm not so sure. My guess would be to do the samething I did above? (there are multiple xy coordinates on the graphs in my text book).

Thanks!

2. Mar 18, 2003

### Zefram

I'm sorry, what's your question? What a slope of 0 means graphically? Or the deal with the whole concept of slope in general?

3. Mar 18, 2003

### RuroumiKenshin

I meant to ask how to measure the slope on a graph.[?]

4. Mar 18, 2003

### Mulder

To find the slope of a straight line through two coordinates find the change in the y-coordinate and divide by the change in x-coordinate. You'll probably need to be more specific....

5. Mar 18, 2003

### RuroumiKenshin

[sigh], I guess I'll try to ask my teacher
(and he's not the best at explaining) ...i can't be specific on something I don't understand....

6. Mar 18, 2003

### RuroumiKenshin

Is my work(on my very first post on this thread) similar to what you're specifying?

***A spark of hope***

7. Mar 18, 2003

### Mulder

Re: slopes!!??

Actually I don't follow this notation...
Can you explain what you have tried to do?

8. Mar 18, 2003

### Zefram

Slope on a graph is rise over run. So if you've got a line that moves up three units every time you move over one unit in the positive x direction, then the slope will be the rise (3) over the run (1) = 3/1 = 3. That's a steeper slope than, say, a line that moves up one unit (rise) every time it moves over three units (run) in the positive x direction--this slope would be 1/3.

Ugh, that was pretty nonmathematical sounding, huh?

9. Mar 18, 2003

### RuroumiKenshin

I GOT IT!! now for questions:

is the run always 1?

10. Mar 18, 2003

### RuroumiKenshin

actually, the two notations are one. there was supposed to be
a fraction bar seperating the notations.

11. Mar 18, 2003

### Integral

Staff Emeritus
No the run does not have to be 1, it is just easy to work with. If the slope is something like 3/5, that means up 3 when your run is 5, you could say the run is 2.5, and rise is 1.5. the key is that the ratio remains the same for a given line. That means a line has a constant slope. No matter where you measure it you will get the same result. No matter how big your run the RATIO of rise/run remains the same.

12. Mar 18, 2003

### RuroumiKenshin

can the slope be angular(consist of right angles in particular)?

13. Mar 18, 2003

### enigma

Staff Emeritus
Yes, to get the angle for rise over run, simply take arctan (rise/run)

tangent is opposite side over adjacent side to the angle you are measuring. The opposite side is the rise, the adjacent side is the run.

The right angles depend.

If the angle is 0, that would correspond to a slope of 0.

If the angle is 90, then the slope is undefined, because it is no longer a function (multiple values in y for a specific value x)

Last edited: Mar 18, 2003
14. Mar 19, 2003

### pmb

The "slope" of a line basically tells you how steep the line is.

I tried drawing some lines as examples but the HTML yanks out spaces so it didn't work - sorry.

The sign of a lines slopw indicates whether the line slopes up or down [ where up and down means starting at the left most part of the line and seeing if the point on the line moves upr or down as you move to the right]. A "+" sign means it slopes up and a "-" sign means it slopes down. If it has no slope (i.e. slope = 0) then it netier goes up nor down. Thus the line

***********

has zero slope. To measure the slope we look at a particular portion of the line - Then we use the "change in rise" and compare it to the "change in run" for that part of the line. And as you can see just by looking at a line it doesn't matter what part of the line or how much of the line you choose. To make this clear use the symbols

dy = "Change in rise"
dx = "Change in run"

and define then as follows: For *any* two points A and B on the line A(X_a, Y_b) and B(X_b, Y_b) where A is a point to the left of B. By "to the left of B" I mean that we choose A as the one such that X_a < X_b. If X_a = X_b then the line is said to have infinite slope (infinite steepness).

dx = X_b - X_a
dy = Y_b - Y_a

Then "define" the quantity "m" as the slope and it has the value

m = dy/dx

Play with it a bit and try using different points. If you have further questions I'd be more than happy to explain further.

Pete

15. Mar 19, 2003

### RuroumiKenshin

what is that equation for? I'm guessing is to measure an infinite slope?

thanks a lot you guys!!

now, for transversal slopes....I'm not sure what they are..I know what a transversal line is but not a transversal slope (are they the same?)

16. Mar 19, 2003

### RuroumiKenshin

so "arctan" means rise/run?

OKAY,functions! I'm not 2 sure about them either (I don't have the best math teacher...)

17. Mar 19, 2003

### Tom Mattson

Staff Emeritus
As to m=dy/dx...

No, that's for any slope. I'm guessing that pmb doesn't know how to make a "delta" in this forum (neither do I). It simply says that the slope (m) of a line is equal to the change in y over the change in x.

No, "slope" means rise/run. "arctan(x)" is the inverse of tan(x). I seriously doubt that you need to worry about it.

18. Mar 19, 2003

### Staff: Mentor

dy = delta y = change in y = rise
dx = delta x = change in x = run
m = slope

dx/dy = rise/run = slope = m

That notation is generally not used until calculus though. And people here tend to have trouble lowering the level of their explanations (no offense, but it is a real problem and not just in here).

The simplest way I can give you for slope between two points:

(x1,y1),(x2,y2)

(y2-y1)/(x2-x1) = slope

On a graph, you can pick any points along the line, but its best to pick points that make the math as easy as possible. If the line starts at the origin (0,0) use that point for your first point.

19. Mar 19, 2003

### RuroumiKenshin

Why shouldn't I worry about it?
what's tan(x)?

20. Mar 19, 2003

### Zefram

You're in pre-algebra, correct? You won't need to know that for a while.

21. Mar 19, 2003

### RuroumiKenshin

Well, I still want to learn about. I'm 13, into theo. physics...and I'm not supposed to worry about whether or not the universe is infinte or if time travel using closed time loops is possible or not unitl I'm MUCH, MUCH older. Preferrably, the only way I am going to learn easily would be to go at MY speed, which is very rapid. If no one here won't tell me, I will learn what it is sooner or later (it will be soon!)

22. Mar 19, 2003

### Tom Mattson

Staff Emeritus
And you will, in good time.

In the first post of your thread you said, in reference to slopes of lines, "I just don't get it!"

That means you've got a way to go before learning about trigonometry, which is prerequisite for the inverse trigonometric functions, about which you are now inquiring.

Your curiosity is great, but there is no illuminating way to render a 'pop' account of trigonometry, as there is in theoretical physics. Learning math and physics is like building a house: It all starts with a solid foundation.

Master algebra and geometry. Then you will get to trig.

That's my $0.02. 23. Mar 19, 2003 ### RuroumiKenshin Okay, Tom, you're right! I've moderately mastered the concept today. Okay, it's no longer a weak point. So, what else should I start learning next? Suggestions? 24. Mar 19, 2003 ### chroot Staff Emeritus This thread reminds me of a fact I've experienced over the course of my (still relatively short) life: The more I learn, the more I realize I don't yet know. - Warren 25. Mar 19, 2003 ### Tom Mattson Staff Emeritus Yes, finish the book. You say that your preferred pace is 'rapid', right? OK, so outpace the class if you need to. Do as many problems as you can. Ask questions. Then, just like a for...next loop in a computer program, do that for as many math and physics courses as you can. The normal progression in upper-track high school math is like this: *Algebra *Plane and Solid Geometry *College Algebra/Trig (also called Precalculus) *Calculus with Analytic Geometry *Multivariable Calculus (if you're advanced enough. I wasn't ) Something I did to help myself out was get into Schaum's Outlines, which are the greatest thing since sliced bread. They are an inexpensive (~$15/each) "Cliff's Notes" version of a textbook, but the fact that they have a ton of solved problems makes up for the lack of detail. In fact, many details are reserved for the solved problems section. I learned algebra-based physics this way, before even taking the course.

If your coursework is not enough for you, then I say get the one entitled Geometry. It has no prerequisites except a logical mind.

There, that's my \$0.04.