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## Integrated math 1

### Course: Integrated math 1 > Unit 4

Lesson 2: Slope- Intro to slope
- Positive & negative slope
- Worked example: slope from graph
- Slope from graph
- Graphing a line given point and slope
- Graphing from slope
- Calculating slope from tables
- Slope in a table
- Worked example: slope from two points
- Slope from two points
- Slope review

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# Calculating slope from tables

Practice calculating the slope of a line given some points on the line shown in a table.

## Want to join the conversation?

- I don't get y over x. Can someone explain it to me?0:27(19 votes)
- Remember rise/run. Check it out on the video
*Worked example: slope from graph*. To find the slope, you take the*change in y/change in x*.(17 votes)

- who else is watching in quarantine for online school classes?(14 votes)
- HURRAY, LOCKDOWN IS OVER!

(lockdown ended june 2020, however our world is forever changed)(3 votes)

- If you get negative and negative. It's positive(3 votes)
- Yes, it's positive. Here's a table if you need help:

Positive*Positive = Positive

Positive*Negative = Negative

Negative*Positive = Negative

Negative*Negative = Positive(17 votes)

- whos watching in 2023?(10 votes)
- I just don't understand this math(5 votes)
- I am having trouble understanding how to find the number difference.(2 votes)
- Im using the first example here to demonstrate. You have to see the difference between x/y point 1 and x/y point 2. If x1 is 2 and x2 is 5, that's +3, so you would write 3. If y1 is -4 and y2 is -5, that's a difference of -1. The slope would then be -1/3(2 votes)

- when you get negitive and negitive. its positive(1 vote)
- I am assuming you are saying that a -/- gives a positive which you are correct.(4 votes)

- Why do we calculate slope as y/x not x/y?(2 votes)
- It makes most sense on a graph. If you start with s slope of 1, it is at a 45 degree angle where y=x. As the slope increases, it makes sense to me that the line will get steeper and steeper (a slope of 2 should be more steep than a slope of 1). A slope of two requires you to go up 2 (y change) /1 (x change). IF you tried flipping it over, as the slope gets closer to the x axis, the slope would get bigger and bigger to reach infinite slope, and thus you would have an infinite slope between negative and positive slopes, but this too does not make sense because 0 is between negative and positive numbers.(2 votes)

- Did anyone else notice that the x coordinates taken separately and the y coordinates taken separately form 2 separate arithmetic progressions?(2 votes)
- hey, i did not until I saw this comment, that is a cool thing to point out.(1 vote)

- amazing slope(2 votes)

## Video transcript

- [Instructor] We are asked, what is the slope of the line
that contains these points? So pause this video and see
if you can work through this on your own before we do it together. Alright, now let's do it together, and let's just remind
ourselves what slope is. Slope is equal to change in y, this is the Greek letter delta, look likes a triangle, but it's shorthand for change in y over change in x. Sometimes you would see
it written as y2 minus y1 over x2 minus x1 where you could kind of view
x1 y1 as the starting point and x2 y2 as the ending point. So let's just pick two xy pairs here, and we can actually pick any two if we can assume that this is
actually describing a line. So we might as well
just pick the first two. So let's say that's our starting point and that's our finishing point. So what is our change in x here? So we're going from two to three, so our change in x is
equal to three minus two which is equal to one, and you can see that
to go from two to three you're just adding one. And what's our change in y? Our change in y is our finishing y one minus our starting y four, which
is equal to negative three. And you could of, you didn't
even have to do this math, you would have been able to see to go from two to three you added one, and to go from four to one,
you have to subtract three. For there we have all
the information we need. What is change in y over change in x? Well, it's going to be, our change in y is negative three and our change in x is one. So our slope is negative
three divided by one is negative three. Let's do another example. Here we are asked, what is the slope of the line that contains these points? So pause this video and see
if you can figure it out or pause the video again and
see if you can figure it out. Alright, so remember, slope
is equal to change in y over change in x. And we should be able to
pick any two of these pairs in order to figure that out if we assume that this is indeed a line. Well, just for variety, let's
pick these middle two pairs. So what's our change in x? To go from one to five, we added four. And what's our change in y? To go from seven to 13, we added six. So our change in y is six
when our change in x is four. And I got the signs right,
in both case it's a positive. When x increases, y increased as well. So our slope is six fourths, and we could rewrite that if we like. Both six and four are divisible by two, so let be divide both the
numerator and the denominator by two and we get three
halves, and we're done.