Main content

## Algebra 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

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Calculating slope from tables

CCSS.Math:

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(20 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*.(16 votes)

- who else is watching in quarantine for online school classes?(12 votes)
- HURRAY, LOCKDOWN IS OVER!

(lockdown ended june 2020, however our world is forever changed)(1 vote)

- 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(8 votes)

- I may be asking a too advanced question but how to we solve if our numbers on our table are

Ex:

2 3 5 6

-3 0 5 8

Please help me(1 vote)- Hi,

So based on your table, I'm guessing the points are (2, -3), (3, 0), (5, 5), and (6, 8).

You can pick any 2 random coordinates. I picked (3, 0) and (5, 5). The equation to find the slope is y2-y1/x2-x1. In this case, y2 is 5 and y1 is 0. x2 is also 5 and x1 is 3. You can substitute this into the question. 5-0/5-3 = 5/2 = 2.5

The final answer is 2.5 or 5/2.(3 votes)

- whos watching in 2023?(3 votes)
- I am!

(but why did u get banned on roblox? and if u got banned, why should I trust ur robux business?)(1 vote)

- I don't completely understand these types of equations. It would be really great if I could get some tips :)(2 votes)
- To calculate the slope, the main thing we do is calculate what is called the "rise over run". It is the difference of the vertical length divided by the horizontal length. With a table, first choose two given values of the y-axis and subtract one value from the other to find the average vertical movement. Then subtract two given values of the x-axis (that were used as the values which produced those y-values) and find their difference. Now divide the difference of the y-values by the difference between the values. Note that if you have a positive divided by a negative, or a negative divided by a positive, the slope will be negative.

As an example, let's say that for every distance of positive 1 you move in horizontal, you go up a distance of 2. Even if you are only given the coordinates (3, 6) and (7, 14) you subtract 14 by 6 to have 8 as the numerator, and subtract 7 by 3 to have 4 for the denominator. Then you divide 8 by 4 for the slope, which is now seen as 2.

To find the correct slope, just make sure that the x-values correspond to their respective y-values(1 vote)

- I straight up can’t do the practice. They are all blank, the hints say = .(2 votes)
- Try refreshing the page, if that doesn't work, try logging out and then logging in again. And if that doesn't work then try powering down your device. If that doesn't work, try seeing if there are other online math outings that could help you.(1 vote)

- For clarification purposes, I
*AM*supposed to simplify-right?

Edit: Ya know I don’t get it- like**AT ALL**. Someone help me...(2 votes) - How do you know when to make it a negative?(1 vote)
- When either the x numbers only add up to 1:

x: 1,2,3,4

y: 10,8,6,4

Since the y is subtracting 2 and the x is adding up 1 the answer would be -2/1. Hope this helps. If not let me know because I am happy to help.(2 votes)

- Will the chart go on forever? Or is it just those 8 numbers? 🤔(1 vote)
- It is possible for the chart to go on forever.

Because we know at least one point on a graph and a slope, we can make up any Y number and figure out X, and vice versa. Thus extending our table as long as we want or graphing the line and picking corresponding (x,y) coordinates directly from a graph.(3 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.