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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.

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• What if my slope is 3/3. can I write 1?
• Absolutely! When the numerator and denominator are the same, its one! Unless one of the numbers are negative, then write -1
• 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
• 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!
• how do you solve for the slope without a graph
• 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.
• 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 :)
• So can we pick ANY points on the line, because I always get confused on what to do when there is no points.
• Find two lattice points, and use those
• 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......
• Yes, it is related
• So is the rise over run same as the unit rate?
• 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!
• 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?
• 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!