Algebra: Slope Figuring out the slope of a line
⇐ Use this menu to view and help create subtitles for this video in many different languages.
You'll probably want to hide YouTube's captions if using these subtitles.
- Welcome to the presentation on figuring out the slope.
- Let's get started.
- So, let's say I have two points.
- And, as we learned in previous presentations, that all
- you need to define a line is two points.
- And I think if you think about that, that makes sense.
- Let's say we have two points.
- And let me write down the two points we're going to have.
- Let's say one point is, why isn't it writing.
- Sometimes this thing acts a little finicky.
- Oh, that's because I was trying to write in black.
- Let's say that one point is, negative 1, 3.
- So, let's see.
- Where do we graph that?
- So, this is 0, 0.
- We go negative 1, this is negative 1 here.
- And then we're going to go 3 up.
- 1, 2, 3.
- Because this is 3 right here.
- So, negative 1, 3 is going to be right over there.
- OK, so that's the first point.
- The second point, I'm going to do it in a different color.
- The second point is 2, 1.
- Let's see where we would put that.
- We would count 1, 2.
- This is 2, 1.
- Because this is 1.
- So the point's going to be here.
- So we've graphed our two points.
- And now the line that connects them, it's going to look
- something thing like this.
- And I hope I can draw it well.
- 35 00:01:36,3 --> 00:01:39,078 Through that point.
- Like that.
- Then I'm going to do it.
- And then I'm just going to try to continue the line from here.
- That might be the best technique.
- Something like that.
- 42 00:01:57,68 --> 00:01:58,57 So, let's look at that line.
- So what we want to do in this presentation is, figure out
- I think will help you.
- So, there's a couple ways to view slope.
- I think, intuitively, you know that the slope is the
- inclination of this line.
- And we can already see that this is a
- downward sloping line.
- Because it comes from the top left to the bottom right.
- So it's going to be a negative number, the slope.
- So you know that immediately.
- And we'll have -- what we're going to do is figure out how
- to figure out the slope.
- So the slope, let me write this down, slope and -- oftentimes
- they'll use the variable m, for slope, I have no idea why.
- Because m, clearly, does not stand for slope.
- That is equal to -- there's a couple of things
- you might hear.
- Change in y over change in x.
- That triangle, which is pronounced, delta just a Greek
- letter, that means change.
- The change in y over change in x.
- And that also is equal to rise over run.
- And I'm going to explain what all of this means in a second.
- So let's start at one of these points.
- Let's start at this green point, negative 1, 3.
- So how much do we have to rise and how much do we have to run
- to get to the second point, 2, 1?
- So let's do the rise first.
- Well, we have to go minus 2, so that's the rise.
- So the rise is equal to minus 2.
- Because we have to go down 2 to get to the same y
- as this yellow point.
- And then we have to run right there.
- We have to run plus 3.
- So rise divided by run is equal to minus 2 over 3.
- Well, how would we do that if we didn't have this nice graph
- here to actually draw on?
- Well, what we can do is, we can say let's take this
- as a starting point.
- Change in y, change in y, over change in x, is equal to
- we take the first y point, which is 3.
- And we subtract the second y point, which
- is 1, you see that?
- We just took 3 minus 1.
- So that's the change in y over, and we take the first x point.
- Negative 1, minus the second x point, minus
- 2, so 3 minus 1 is 2.
- And negative 1 minus 2 is equal to minus 3.
- So, same thing.
- We got minus 2 over 3.
- Now we could have done it the other way.
- And I'm running out of space here.
- But we could've made this the first point.
- If we made that the first point, then the change in y
- would have been -- I want to make it really cluttered,
- so to confuse you.
- Change in y would be this y.
- 1 minus 3 over change in x, would be 2, minus minus 1.
- Well, 1 minus 3 is minus 2.
- And 2 minus negative 1 is 3.
- So, once again, we got minus 2/3, So it doesn't matter which
- point we start with, as long as, if we use the y in this
- coordinate first, then we have to use the x in that
- coordinate first.
- Let's do some more problems.
- Actually, I'm going to do a couple just so you see the
- algebra without even graphing it first.
- 113 00:05:22,45 --> 00:05:24,56 So, let's say I wanted to figure out the slope between
- the points 5, 2, and 3, 5.
- Well, let's take this as our starting point.
- So, change in y over change in x, or rise over run, well,
- change in y would be this 5.
- 5 minus this 2.
- Over this 3 minus this 5.
- And that gets us 3, this is a 5, over minus 2.
- Equals minus 3/2.
- Let's do another one.
- This time I'm going to try to make it color-coded so it'll
- more self-explanatory.
- Say, it's 1, 2.
- That's the first point.
- And then the second point is 4, 3.
- So, once again, we say slope is equal to change in
- y over change in x.
- Well, in y.
- We take the first y.
- Let's start here.
- And we'll call that y1.
- So that's 3 minus the second y, which is that 2.
- And then all of that over, once again, the first x.
- Which is 4, minus the second x, which is that 1.
- And this equals 3 minus 2, is 1.
- And 4 minus 1 is 3.
- So the slope in this example is 1/3.
- And we could have actually switched it around.
- We could have also done it other way.
- We could have said, 2 minus 3 over 1 minus 4.
- In which case we would have gotten negative
- 1 over negative 3.
- Well, that just equals 1/3 again.
- Because the negatives cancel out.
- So I'll let you think about why this and this come
- out to the same thing.
- But the important thing to realize is, if we use the 3
- first, if we use the 3 first for the y, we also have to
- use the 4 first for the x.
- That's a common mistake.
- And also, you always have to be very careful with the negative
- signs when you do these type of problems.
- But I think that will give you at least enough of a sense that
- you could start the slope problems.
- The next module, I'll actually show you how to figure
- out the y intercept.
- Because, as we said, before the equation of any line is,
- y is equal to m x plus b.
- And I'm going to go into some more detail.
- Where m is the slope.
- So if you know the slope of a line.
- And you know the y intercept of a line, you know everything you
- need to know about the line, and you can actually write down
- the equation of a line, and figure out other points
- that are on it.
- So I'm going to do that in future modules.
- I hope I haven't confused you too much.
- And try some of those the slope modules.
- You should be able to do them.
- And I hope you have fun.
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.
Discuss the site
For general discussions about Khan Academy, visit our Reddit discussion page.
Flag inappropriate posts
Here are posts to avoid making. If you do encounter them, flag them for attention from our Guardians.
abuse
- disrespectful or offensive
- an advertisement
not helpful
- low quality
- not about the video topic
- soliciting votes or seeking badges
- a homework question
- a duplicate answer
- repeatedly making the same post
wrong category
- a tip or feedback in Questions
- a question in Tips & Feedback
- an answer that should be its own question
about the site
Share a tip
Suggest a fix
Have something that's not a tip or feedback about this content?
This discussion area is not meant for answering homework questions.