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This is part two on working with a slope of a line and we're going to just do some more
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practice by looking at a graph, computing the exact slope of the line.
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So the first thing to notice is the slant of the line.
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This is like going downhill.
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If you go from left to right, if your eyes move from left to right, remember this is going
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to be a negative slope.
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So if you keep that in mind, it's going to be a negative slope, then when you're done
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with your problem, make sure that your answer is negative.
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All right, so what we could do is start from any point on the line and figure out how
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to get to another point on the line.
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Remember, it doesn't matter where you start and where you end as long as those two
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points are on the line.
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Let's go ahead and start right here.
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Okay, and let's say we want to end over here.
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All right, how would I get from that point to the other point?
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Now, if you'd like to do the rise going up or down first and then the run, that's fine.
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I just from habit, always do the denominator first.
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I do the run first.
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I go left to right first.
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So I first have to go to the right, how many blocks or how many spaces.
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All right, if I count them very carefully, that's four plus four more.
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I've got eight spaces and I'm going to the right.
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So in the run, the x value is eight, the x coordinate, if you want to think of it, actually
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not the x coordinate, just the run, the change in x.
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And now I'm going to go down, all right, that's going to be my rise even though I'm going
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down.
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Down means it's negative two.
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So that's going to be negative two.
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And now we simplify it.
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Remember, the slope is just a number.
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It's negative one-fourth.
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So the slope of this line is negative one-fourth.
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Now let's try it between two other points.
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So let's pick a couple other points and do exactly the same thing.
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See if I can get rid of the...
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Okay.
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So here we are.
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I've got the line again.
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And let's go between these two points.
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And remember, it doesn't matter where you start and where you end.
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So let's say I'm going to start at this one that's on the y axis and I need to get over
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to the left.
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So how am I going to do that?
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First I've got to go to the left.
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How many spaces?
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Negative four.
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So this time in the x direction, the run, I'm going negative four spaces.
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And then I'm going up one space to get to that point.
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So this plus one and that also reduces to negative one-fourth.
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It doesn't matter what two points you use is going to keep happening.
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The slope of this line is going to be negative one-fourth.
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So we'll try another line now.
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Here's another one.
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I want you to figure out the slope of the line.
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I didn't draw this line exactly perfectly, but hopefully you can see the little dot.
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So go ahead and put the video on pause and see if you get for the slope of this line.
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You can do the rise over run between any two points.
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OK.
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There's lots of ways to do it.
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Let's say I just pick this point and this point.
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I'm going over two spaces and I'm going up two spaces.
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So the slope, well they're both two.
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Two over two is going to be one.
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So hopefully you got a slope of one.
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Remember, it's just a number.
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Ready for another one?
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So it seems easier to see the points.
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I'm actually not going to draw the line.
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But imagine you have a line going through the four points I've shown here.
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So there are different ones you can go from.
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You've got zero, five.
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Another order pair here is one, two.
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The order pair is two negative one and another one is three negative four.
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So pick two points.
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Doesn't matter.
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I'm figuring out how would you get from one point to the other.
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Put it on pause and try it.
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First of all, I hope you notice that this line is going to be like going downhill as you
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look from left to right.
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So the slope is going to be negative.
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So hopefully you'll notice that when you're done, that you got a negative number.
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All right, let's pick these two points in the middle here.
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I want to go from here to here.
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How would I get there?
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I would have to go in the x direction, positive one, and in the y direction, negative three.
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So if I was going to do that slope in the x direction, that goes in the denominator,
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right?
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Positive one in the y direction, negative three, that gives me a slope of negative three.
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All right, let's say somebody else picked two other points.
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How about this one up here and this one down here and let's start at the bottom and try
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to get up here.
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So I first have to go to the left.
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How many spaces?
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Three spaces.
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So I know that's what's going to go in the denominator.
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And then I got to go up all the way to here.
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So we count the spaces here.
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There's four plus five more.
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That's nine spaces.
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Nine divided by negative three is also negative three.
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So the slope of this line through those four points is a slope of negative three.
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So if I had graphed the line carefully, that's hard to do, something like this, that blue
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line, if it was straight, has a slope of negative three.
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Notice that we determined ahead of time that the slope was negative.
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The slope was less than zero because it slams the direction which makes it less than
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zero.
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So it looks like we did it correctly.
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We did it two different ways.
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All right.
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How about this horizontal line?
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During number, what the slope of a horizontal line is?
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We went over it in the previous video.
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It was zero.
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But let's verify that.
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So in other words, you could remember that a horizontal line has slope zero.
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But it should also work by using our formula of rise over run.
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So let's pick two points.
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Let's pick this point and this point here.
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All right.
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So how am I going to get from this point over to that point?
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Well, first I've got to go over four spaces.
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So I know over, that's what it goes over, four spaces is in the denominator, the x.
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And then I don't go up or down at all, do I?
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So it's zero.
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And what's zero over four?
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Zero.
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So we verified it.
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The slope really is zero.
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Let's do it for a vertical line.
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Remember what the slope of a vertical line is?
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It should be end defined.
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It is an equal and define you say slope is end defined.
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All right, but let's verify that.
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Let's pick two points about this point and this point.
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All right.
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So the rise, let's do the rise first.
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In other words, how far up or down?
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Let's say if I start at the top and I want to get down.
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I'm going down five spaces.
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All right.
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So in that direction, I'm going down five.
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And that's the vertical, the rise goes in the numerator.
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And then what?
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How far over left or right am I going?
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Why I'm not going left or right at all?
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And now you got to remember what's anything divided by zero and defined.
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If you're not sure about that, look at my video about why dividing by zero is undefined.
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So that's the conclusion of this video.
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We were just practicing figuring out the slope of a line by looking at a graph of it.
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Sometimes it's not so easy and you're just given two points on a line as order pairs.
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So the next video is going to go over how to compute it algebraically without looking
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at a picture.