Slope of a line 2 Slope of a Line 2
Slope of a line 2
- Find the slope of the line that goes through the ordered
- pairs (4, 2) and (-3, 16).
- So just as a reminder, slope is defined as rise over run
- or you could view that as rise is just a change in y
- and run is a change in x
- The triangles here, there's the delta symbol
- it literally means "change in"
- Or another way, and you might see this formula and
- it tends to be really complicated
- but just remember it's just these two things over here
- Sometimes slope will be specified with the variable m
- and they'll say m is the same thing
- (and this is really the same thing as change in y)
- They'll write y2 minus y1 over x2 minus x1
- And this notation tends to be kind of complicated
- but all this means is you take the y value of your endpoint
- and subtract from it the y value of your starting point
- That'll essentially give you your change in y
- and it says take the x value of your endpoint
- and subtract it from the x value of your starting point
- and that'll give you your change in x
- So whichever of these work for you, let's actually
- figure out the slope of the line that goes through these
- two points.
- So we're starting at
- (actually we can do it both ways)
- we can start at this point and go to that point and calculate the slope,
- or we can start at this point and go to that point and calculate the slope.
- So let's do it both ways.
- So let's say our starting point is the point (4,2)
- And let's say our endpoint is (-3, 16)
- So what is the change in x over here
- What is the change in x in this scenario
- So we're going from 4 to -3
- if something goes from 4 to -3, what was its change?
- You have to go down 4 to get to zero
- Then you have to go down another 3 to get to -3.
- So our change in x here is -7
- Actually, let me write it this way
- Our change in x is equal to -3 - 4 which is equal to
- If I'm going from 4 to -3, I went down by 7
- Our change in x is -7
- Let's do the same thing for the change in y
- And notice: I implicitly use this formula over here
- our change in x was this value - our endpoint
- our end x value minus our starting x value
- let's do the same thing for our change in y
- Our change in y
- If we're starting at 2 and we go to 16 that means
- we moved up 14
- Or another way you could say it is:
- You could take your ending y value
- and subtract from the your starting y value
- and you get 14
- So what is the slope over here?
- Well the slope is just change in y over change in x
- So the slope over here is change in y over change in x
- which is: our change in y is 14
- and our change in x is -7
- And if we want to simplify this 14 divided by -7 is -2
- Now what I want to show you is we could have done it
- the other way around
- We could have made this the starting point and this the endpoint.
- And what we would have gotten is the negative values
- of each of these, but they would have cancelled out
- and we would still get -2.
- Let's try it out. So let's say that our start point
- was (-3,16) and let's say that our endpoint is (4,2)
- So in this situation, what is our change in x?
- Our change in x.
- If I start at -3 and I go to 4, that means I went up 7
- Or if you want to just calculate that, you would do 4 - -3
- but needless to say, we just went up 7
- And what is our change in y
- Our change in y over here
- Or you could say our "rise"
- If we start at 16 and we end at 2, that means we
- went down 14.
- Or you could just say 2 - 16 is -14.
- We went down by 14 - this is our run.
- So if we say rise over run, which is the same thing as change
- in y over change in x.
- Our rise is -14 and our run here is 7.
- So notice these are just the negatives of these values from
- when we swapped them.
- So once again, this is equal to -2.
- Let's just visualize this - let me do a quick graph here
- just to show you what a downward slope would look like
- So let me draw our two points
- So this is my x axis
- That is my y axis
- So this point over here, (4,2), so let me graph it
- So, we're going to go all the way up to 16, so let me save some space here
- So we have 1, 2, 3, 4
- it's 4 comma 1 ... 2
- So (4,2) is right over here
- Then we have the point (-3, 16)
- So let me draw that over here
- So we have -1 ... 2 ... 3
- and we have to go up 16, so this is 2 ... 3 ... 4 ... 5 ... 6 ... 7 ... 8 ... 9 ... 10 ... 11 ... 12
- 13 ... 14 ... 15 ... 16
- So it goes right over here
- So this is (-3,16).
- So the line that goes between them is going to look something like this
- I'm going to try my best to draw a relatively straight line
- That line will keep going.
- So that's my best attempt.
- And notice it's downward sloping - as you increase in x
- value the line goes down.
- It's going from the top left to the bottom right
- As x gets bigger, y gets smaller
- that's what a downward sloping line looks like
- And just to visualize our change in x's and our change in y's
- that we dealt with here,
- when we started with (4,2) and ended at (-3,16)
- That was analogous to starting here and ending over there
- And we said our change in x was -7
- We have to move back our run
- We had to move in the left direction by 7
- That's why it was -7
- And then we had to move in the y direction positive 14
- That's why our rise was positive
- So it's 14 over -7, or -2.
- When we did the other way, we started at this point, and ended at this point
- Started at (-3,16) and ended at that point.
- So in that situation our run was positive 7
- And now we had to go down in the y direction since we
- switched the starting and the end point.
- And now we have to go down -14.
- Our run is now positive 7, and our rise is now -14
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
Have something that's not a question about this content?
This discussion area is not meant for answering homework questions.
Share a tip
When naming a variable, it is okay to use most letters, but some are reserved, like 'e', which represents the value 2.7831...
Thank the author
This is great, I finally understand quadratic functions!
Have something that's not a tip or thanks about this content?
This discussion area is not meant for answering homework questions.
At 2:33, Sal said "single bonds" but meant "covalent bonds."
For general discussions about Khan Academy, visit our Reddit discussion page.
Here are posts to avoid making. If you do encounter them, flag them for attention from our Guardians.
- disrespectful or offensive
- an advertisement
- low quality
- not about the video topic
- soliciting votes or seeking badges
- a homework question
- a duplicate answer
- repeatedly making the same post
- a tip or thanks in Questions
- a question in Tips & Thanks
- an answer that should be its own question