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# Worked example: slope from graph

The slope of a line is rise over run. Learn how to calculate the slope of the line in a graph by finding the change in y and the change in x. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• What if my slope is 3/3. can I write 1?
(53 votes)
• Absolutely! When the numerator and denominator are the same, its one! Unless one of the numbers are negative, then write -1
(80 votes)
• hey... I am bad at math and this is my last chance to pass. I do not have any ckue what to do? i need major help
(33 votes)
• ok here we go! slope is the change in y over change in x! so lets say you have a point here (3,5) which means 3x and 5y so lets say theres another point at (8,7) , you need to find the slope so how many did you change in y from 5 to 7? 2! how many did you change from 3 to 8? 5! so the slope is 2/5! and the y-intersept is where the x is equal to zero! so lets say the point goes through(0,2) it would be y= 2/5+2! hope this helped!
(65 votes)
• how do you solve for the slope without a graph
(30 votes)
• This is so hard to understand. Really can't believe Im failing to understand something being explained by Sal because before I understood all of them.
(14 votes)
• I can try to explain it :)

In technical terms, the slope of the line is the change in y over the change in x. But I just like to think of it as rise over run.

To find the slope of the line, pick two points on the line. Let's say we've looked at our graph, and have picked the points (3, 2) and (5, 6).

Let's find how much the change in x aka the run is. To do that, we take the point with the greatest x value:
(5,6)
Find the x value of that point:
5
and subtract the x value of the other point. (The other point is (3,2) so the x value of the other point is 3):
5-3 = 2
So, our change in x aka run is 2.

Now let's find the change in y or rise. To do that, we take the y value of our first point (our first point is (5, 6) so the y value is 6):
6
And subtract the y value of the other point (the other point is (3,2) so the y value is 2):
6-2=4
So our change in y or rise is 4.
Now we can finish by putting the rise over run :D
Rise = 4
Run = 2

Slope = 4/2
simplify
Slope = 2/1
simplify again
Slope = 2
And there we have it! :D
Hope this helps :)
(32 votes)
• So can we pick ANY points on the line, because I always get confused on what to do when there is no points.
(18 votes)
• Find two lattice points, and use those
(7 votes)
• i almost got it correct this time after repeated attempts but my problem was about the negative sign and counting how many steps we move backward......i mean is the negative sign related to how many steps we move backward in the graph? It would be nice if someone clarified it out for me......
(8 votes)
• Yes, it is related
(5 votes)
• So is the rise over run same as the unit rate?
(6 votes)
• I'm pretty sure rise over run is the same as unit rate, if you had a graph where x is say time ( years), and is the amount of money earned per year, the graph might have a slope ( rise over run ) of 200 dollars every 1 year. So if you think about it, yes rise over run ( slope ) is the same as unit rate. However, sometimes your slope might be a fraction like 1/2, in this case you could make it 0.5/1, or keep it as 1/2. I hope I helped! Please feel free to correct me as i am learning too!
Good Day!
(13 votes)
• Is a slope always for a linear segment? and what will we use if the line is non linear?
(9 votes)
• That's what a lot of calculus is about. There's not a simple answer to that if you don't know calculus.
(9 votes)
• I have a question I know that you can pick any points for the slope. I did practise and I chose points and it was incorrect. How to you know the exact slope for a problem?
(9 votes)
• Hmm, I'm not sure if this is what you're asking but I think you are trying to ask how you double-check your work. So let's say, that you got two points and you used those two points to find the slope of the line. If you want to confirm if this is correct, find two other points. Remember, the two points are the rise over run of x and y in a line. Hope this helps!
(3 votes)
• how do you know to measure it by going down or up
(8 votes)
• If it goes up as you move to the right, you should measure it going up. If it goes down as you move to the right, you should measure it going down.
(5 votes)

## Video transcript

Find the slope of the line in the graph. And just as a bit of a review, slope is just telling us how steep a line is. And the best way to view it, slope is equal to change in y over change in x. And for a line, this will always be constant. And sometimes you might see it written like this: you might see this triangle, that's a capital delta, that means change in, change in y over change in x. That's just a fancy way of saying change in y over change in x. So let's see what this change in y is for any change in x. So let's start at some point that seems pretty reasonable to read from this table right here, from this graph. So let's see, we're starting here-- let me do it in a more vibrant color-- so let's say we start at that point right there. And we want to go to another point that's pretty straightforward to read, so we can move to that point right there. We could literally pick any two points on this line. I'm just picking ones that are nice integer coordinates, so it's easy to read. So what is the change in y and what is the change in x? So first let's look at the change in x. So if we go from there to there, what is the change in x? My change in x is equal to what? Well, I can just count it out. I went 1 steps, 2 steps, 3 steps. My change in x is 3. And you could even see it from the x values. If I go from negative 3 to 0, I went up by 3. So my change in x is 3. So let me write this, change in x, delta x is equal to 3. And what's my change in y? Well, my change in y, I'm going from negative 3 up to negative 1, or you could just say 1, 2. So my change in y, is equal to positive 2. So let me write that down. Change in y is equal to 2. So what is my change in y for a change in x? Well, when my change in x was 3, my change in y is 2. So this is my slope. And one thing I want to do, I want to show you that I could have really picked any two points here. Let's say I didn't pick-- let me clear this out-- let's say I didn't pick those two points, let me pick some other points, and I'll even go in a different direction. I want to show you that you're going to get the same answer. Let's say I've used this as my starting point, and I want to go all the way over there. Well, let's think about the change in y first. So the change in y, I'm going down by how many units? 1, 2, 3, 4 units, so my change in y, in this example, is negative 4. I went from 1 to negative 3, that's negative 4. That's my change in y. Change in y is equal to negative 4. Now what is my change in x? Well I'm going from this point, or from this x value, all the way-- let me do that in a different color-- all the way back like this. So I'm going to the left, so it's going to be a negative change in x, and I went 1, 2, 3, 4, 5, 6 units back. So my change in x is equal to negative 6. And you can even see I started it at x is equal to 3, and I went all the way to x is equal to negative 3. That's a change of negative 6. I went 6 to the left, or a change of negative 6. So what is my change in y over change in x? My change in y over change in x is equal to negative 4 over negative 6. The negatives cancel out and what's 4 over 6? Well, that's just 2 over 3. So it's the same value, you just have to be consistent. If this is my start point, I went down 4, and then I went back 6. Negative 4 over negative 6. If I viewed this as my starting point, I could say that I went up 4, so it would be a change in y would be 4, and then my change in x would be 6. And either way, once again, change in y over change in x is going to be 4 over 6, 2/3. So no matter which point you choose, as long as you kind of think about it in a consistent way, you're going to get the same value for slope.