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Graphing sequence relationships

Explore the concept of numerical patterns. Understand how to generate two sequences using given rules, identify relationships between corresponding terms, form ordered pairs from these terms, and graph these pairs on a coordinate plane.  Created by Sal Khan.

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  • orange juice squid orange style avatar for user Jon Winder
    Is there a way to describe both sequences simultaneously in a single expression?
    (13 votes)
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    • piceratops ultimate style avatar for user fr33d0g
      Not really, because you need an equation to describe how x gives you y. To do this you need an equation. 5x by itself would be considered an expression. But that is not enough info to give you the sequence for getting y. You need the "equation" 5x=y to describe the sequences for x and y to plot them. Hope this helps. :)
      (30 votes)
  • piceratops seed style avatar for user Sri Krishna Pandey
    Can anybody tell me why x and y are traditional letters?
    (14 votes)
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    • blobby green style avatar for user MukhtarTuraani
      because coordinate planes is normally used to represent data but when someone is using it with no data the axes are unknown so people use letters to represent the unknown so the axis x is unknown or not assigned and axis y is unknown or not assigned. so people use letters as a placeholder. I wish I helped
      (17 votes)
  • male robot donald style avatar for user GOᗪᔕ ᔕEᖇᐯᗩᑎT #Catholic #Prolife
    Can someone help me? I can't figure out the following challenge Visualizing and interpreting relationships between patterns. If you see this please answer! Thanks for your time
    (6 votes)
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    • leaf green style avatar for user Mark Griffiths
      Think of the plot area as two number lines. The first number in an ordered pair goes to the right and the second number in an ordered pair goes number goes up. (Right UP!). Easy enough to plot on the graph. That's the easy part. The part you might be having problems with is finding out the relationship between the numbers.

      Example

      Sequence X: Start at the number 5 and the rule is add one. So sequence X would read 5, 6, 7, 8, 9 and so on.
      Sequence Y: Start at the number 10 and the rule is add two. So the sequence Y would read 10, 12, 14, 16, 18 and so on.
      Your ordered pairs would be (5,10) (6,12) (7,14) (8,16) (9,18)
      Do you notice a pattern? 5x2=? 6x2=?
      Could you say that the numbers on the Y axis are two times as large? I hope this helps some.
      (9 votes)
  • starky ultimate style avatar for user Deal With It
    what is a constant number? Please reply, I have a test tomorrow...
    (4 votes)
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    • duskpin ultimate style avatar for user lanyanzi
      A fixed value.

      In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.

      Example: in "x + 5 = 9", 5 and 9 are constants

      If it is not a constant it is called a variable.

      I think.
      (8 votes)
  • aqualine ultimate style avatar for user Alex
    Why X and Y and not any other letters?
    (6 votes)
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  • male robot hal style avatar for user Jael Ronaldo
    Good video
    (4 votes)
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  • duskpin tree style avatar for user Keyon
    Can someone help me? I can't figure out the following challenge Visualizing and interpreting relationships between patterns. If you see this please answer! Thanks for your time
    (2 votes)
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  • cacteye green style avatar for user lorenzoc70332
    what are inputs and outputs?
    (3 votes)
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  • mr pants teal style avatar for user Bedazzled Blue
    why does X go first? and how does this apply in real life?
    (0 votes)
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    • starky ultimate style avatar for user Sal
      Hi, the way I usually explain this to my students by comparing it to the rules of the road. Why does everybody drive on the left in the UK (or the right in the US)? Because if everybody drove where they wanted it would be chaos. So I tell my students that mathematicians decided to always write X first. This way, if you had to whatsapp coordinates to someone in Fiji he or she will know what you meant and if they sent you coordinates you would be able to plot them the way the your Fijian friend meant. So it's basically convention so that we can communicate clearly, no matter where we're from.

      How does this apply to real life? Oh, some of the most beautiful maths in the world is based on this. This is one of the first skills that you learn that eventually becomes calculus and calculus is the maths that people used to put a man on the moon and describe the motion of stars*. You are literally on the path to learning rocket science. Isn't that amazing? *(I'm over-simplifying but I think you get the idea).
      (12 votes)
  • female robot grace style avatar for user Isabella.Harmon
    at , it said in the captions wee in stead of we is that a typo or meant to be their
    (1 vote)
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Video transcript

Voiceover: You are given the following starting numbers and rules for two sequences of numbers. The first sequence, Sequence x, starting number should be one, and then the rule is add one. Sequence y, starting number should be five, and then the rule should be add five. Fill in the table with the first three terms of x and y. Then plot the ordered pairs (x,y) on the graph below. So let's see, Sequence x. They say, the starting number, the starting number should be one. So the starting number is one, and then the rule, to get to the next number, you just add one. So, one plus one is two. Two plus one is three. Fairly straight forward. Now, let's look at Sequence y. They're saying the starting number should be five. Starting number five, and then the rule is, to get the next term, we just add five. So, five plus five is ten, ten plus five is fifteen. Now they want us to plot these things. Let's see, we plot them as ordered pairs, so we're going to have the point (1,5). When x is one, y is five. We see that there, x is one, y is five. When x is two, y is ten. When x is two, y is ten, and then when x is three, y is fifteen. When x is three, y is fifteen, and wee see that. For every one we move to the right, for every one we increase in the horizontal direction, every one we increase in x, we increase five for y. We increase one for x, we increase five for y. So now we just have one last thing to answer. The terms in Sequence y are blank, times the terms in Sequence x. So you immediately see, this term, five, is five times one. Ten is five times two. Fifteen is five times three, and it makes sense. You started five times higher, and here you added one each time, and we see that visually right over here, we add one each time, while here we add five times as much each time. We add five each time. The terms in Sequence y are five times the terms in Sequence x. We got it right.