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### Course: 6th grade foundations (Eureka Math/EngageNY)>Unit 4

Lesson 4: Topic E & F: Foundations

# Graphing patterns on coordinate plane

Learn about understanding numerical patterns. Explore how to generate a second pattern from a given one by applying a rule, in this case, multiplying by 3 and adding 1. Then, graph the pairs of corresponding terms from both patterns on a coordinate plane. Created by Sal Khan.

## Want to join the conversation?

• how does he get the answer I don't understand!
• Because it almost like a cooridante plane. A is the x axis and B is the b axis think of it that way
• this doesn't even help with what I need it to help me with
(┬┬﹏┬┬)
• What is the use or the importance of Coordinate Plane?
• 1. Describing position.
2. Location of Air Transport:
An air traffic controller must know the location of every aircraft in the sky within certain geographic boundaries.
3. Map Projections.
4. Latitude and longitude:
A geographic coordinate system is used to assign geographic locations to objects.
5. Military service:
For each target there are coordinates to determine the precise position of them.
6. Economy:
for analysing and managing.
• how do you write the notes for home work
• what is the pattern B supposed to graph?
(1 vote)
• Pattern B represents the y/vertical axis, and pattern A represents the x/horizontal axis.
(1 vote)
• The video is not working right now
(1 vote)
• Oooooohhh! So if you have "a" it is in the x axis and "b" is the y axis?
(1 vote)
• Yes, that is what would usually be done. Though sometimes problems tell you which variable to place on each access when the problem is not using X and Y.
(1 vote)
• Isn't it obvious that there's a pattern of 3 difference in each number?
(1 vote)
• i do not get any of it
(1 vote)
• At Sal started to say things over and over again. IS THAT BAD?
(1 vote)
• think he was trying to make things clear for everyone I mean like you caught that so it was clear maybe he thought the person was kinda distracted at that point like my SISTER is distracting me with dolls (just an example)
(1 vote)

## Video transcript

The following table contains the first five terms of the given Pattern A. Generate Pattern B according to this rule. For every term of Pattern A-- so they give us the terms of Pattern A here-- multiply the term by 3 and add 1 to get the corresponding term of Pattern B. Then graph the pairs of corresponding terms. So for every term in Pattern A, we want to multiply by 3 and 1. So if we multiply 0 by 3, we get 0. And you add 1, you get 1. If you multiply 1 by 3, you get 3. And then you add 1, you get 4. 2 times 3 is 6, plus 1 is 7. 3 times 3 is 9, plus 1 is 10. Remember, we're just multiplying by 3 and adding 1. 4 times 3 is 12, plus 1 is 13. So those are the corresponding terms for Pattern B. And then they ask us to graph them. So let's try to graph these points. So when Pattern A is 0, Pattern B is 1. When Pattern A is 0-- so this is Pattern A equaling 0. That's our horizontal axis, the value of Pattern A-- Pattern B is the value of our vertical axis. Pattern B is 1. When Pattern A is 1, Pattern B is 4. So when Pattern A is 1, Pattern B is 4. Pattern B is on the vertical axis. When Pattern A is 2, Pattern B is 7. When Pattern A is 3, Pattern B is 10, so 3 in the horizontal direction. That's our Pattern A value. And our Pattern B value is 10. And then, finally, when Pattern A is 4, Pattern B is 13. Now, let's just look at these patterns. We see Pattern A is increasing by 1 each time, while Pattern B is increasing by it's-- well, Pattern A starts at 0 and increases by 1, while Pattern B starts at 1 and increases by 3, which makes complete sense. It makes sense that it starts at 1, because all of these, you multiply by 3 and add 1. So you start at 1. And then, the fact that we're multiplying by 3, that's what's leading to the distance between these points being 3. So let's check our answer to make sure we got this right, and we did.