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Slope of a line: negative slope

Slope is like a hill's steepness. We find it by dividing the vertical change (rise) by the horizontal change (run). If we move right on a graph and go up, the slope is positive. If we go down, it's negative. We can find the slope between any two points on a line, and it's always the same. Created by Sal Khan and Monterey Institute for Technology and Education.

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• at Sal says delta. Where does this come from?
• Delta is the fourth letter of the Greek alphabet which is usually used for denoting change between two values. For e.g. Δy means the change or difference between the two values of the y co-ordinates.
• how do I find the slope of a triangle
• Only lines have slope, not shapes. If you want to fund the slope of the sides of triangles, then you'll need to know two coordinate points on the sides and then use the slope formula (change in y)/(change in x).
Example:
There's is a Triangle ABC where A is (0, 0), B is (2, 3), and C is (5, 6). What is the slope of each side of the triangle.
The slope of AB is:
(change in y)_(3-0)
-------------=-----=3/2
(change in x)_
(2-0)
The slope of BC is:
(change in y)_(6-3)
-------------=------=1
(change in x)_
(5-2)
The slope of AC is:
(change in y)_(6-0)
-------------=-----=6/5
(change in x)_
(5-0)

I hope this helps!
• Hey, How do I know if I am suppose to count the slope over the line or under the line between the two points?
• You can do either way. One thing, the signs might differ a little when you're doing the sum, but ultimately, after you simplify the answer, you'll see that whichever direction you went, the answer will be the same.
NOTE THIS: If you're going left, it'll be negative.
if you're going right, it'll be positive.
if you're going downwards, it'll be negative.
if you're going upwards, it'll be positive.
if you don't understand this negative - positive thing, you can check out the topic - Quadrants.
• I'm in high school I've got no clue still how to plot a point could anyone give me any evidence on how to understand it better
• Okay. First let's visualize the coordinate plane (the graph). Going across, we have the x axis. Going up and down we have the y axis. On these axes are numbers. The numbers are spaced evenly. Using these numbers, you can find any point on either of the axes. For example, If I asked you to find 5 on the x axis on the following graph:
``y axis|6|4|2|_ 2 _ 4 _ 6 _ 8 _   <----- x axis``

you would tell me that it is right in between the "4" and the "6" on the x axis. They're just two number lines. Now, to find a point on the plane (that is, a point in the space) you need two numbers: one for it's x location, and one for it's y location. Think of it this way: the x value tells you how far across the point is. If a point has an x value of 4, for example, you know that it is on the number 4 on the x axis, or it is directly above or below the number 4. The same goes for the y value, only this time it tells you how far up the point is.

The only thing we haven't covered is how we notate all of this, and this is quite trivial. If I say point x has coordinates [4,5], that means that it has an x value (or x coordinate) is 4, and the y value (or y coordinate) is 5. On a graph, that would look like this:
``|6|4|       .  <== our point is "4 across" (directly above2                                    number 4) and it is |_  2 _ 4 _ 6 _ 8 _      "five up" (directly across from                                        where the number 5                                        would be).``
• At What does the triangle on x+3 stand for?
• It's not a triangle, it's "delta". In this case it means that you have to find the absolute value of x1 (which is -3) minus x2 (which is 0). The result is 3.
• if x = 19y - 3, is 19 the slope? and how do you solve that?
• It depends on how you look at the problem. Normally mathematicians consider the xy-plane, it is the coordinate system you are probably most familiar with. Another plane is the yx-plane, then your y-axis is pointing to the left/right and your x-axis up/down. In the xy-plane (the coordinate system) we write a line as y=kx+m. The k in the equation y=kx+m is the slope of the line in the xy-plane (the coordinate system). The m in the equation y=kx+m is where the line hits the y-axis (that's like saying "where x=0"). So, if we put in x=0 we get y=k*0+m=m, so m is the value where the line hits the y-axis, just as I told you!

To solve your problem, we do like this.

We look att your equation x=19y-3, we now that the slope here is 19 and where the line hits the x-axis is where y=0, x=19*0-3=-3, so x=-3 is where the line hits the y-axis. But now we are talking about the yx-plane! Lets think about the xy-plane (the usual coordinate system).

So we have x=19y-3, and we want to solve for y.

x=19y-3
x+3=19y
divide by 19
(x+3)/19=y
simplify
x/19+3/19=y
change the order of the equation
y=x/19+3/19

Now our equation is on the form y=kx+m.

Here k=1/19, because x*(1/19)=x/19

and m=3/19
• i did not understood you
• facts
• I have a question about getting slope from a graph, is there a specific location in the slope that i have to pick or is it any point that intersect with the horizontal and vertical grids?
Also does the points have to be in one quadrant?

Because i was doing the problems and it seems they don't allow for more than 2 exact points to be the right answer.
• As long as the line you are measuring the slope of is straight, it will have the same slope everywhere, so it doesn't matter which two points you pick. They don't have to be in the same quadrant, although it's usually easier to pick two points in the first quadrant if you can, though, because then you all positive coordinates and you're not having to worry about subtracting negatives and so on. It can also be easier to pick the points where the line intersects the axes, because there one of the coordinates will be zero, which again makes the subtraction easier. An example: if the two points on the line are (3,0) and (-1,8) then the slope is (8 - 0) / (-1 - 3) = 8 / (-4) = -2.