Slope of a line Slope of a line
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- 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.
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