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## 7th grade (Eureka Math/EngageNY)

### Unit 1: Lesson 2

Topic B: Unit rate and constant of proportionality- Intro to rates
- Unit rates
- Solving unit rate problem
- Solving unit price problem
- Constant of proportionality from equation
- Constant of proportionality from equations
- Identifying constant of proportionality graphically
- Constant of proportionality from graphs
- Constant of proportionality from table (with equations)
- Constant of proportionality from tables (with equations)
- Comparing proportionality constants
- Compare constants of proportionality
- Interpret proportionality constants
- Interpret constants of proportionality
- Worked example: Solving proportions
- Solving proportions
- Writing proportions example
- Writing proportions
- Proportion word problem: cookies
- Proportion word problem: hot dogs
- Proportion word problems
- Equations for proportional relationships
- Writing proportional equations from tables
- Writing proportional equations
- Interpreting graphs of proportional relationships
- Identify proportional relationships from graphs
- Interpreting graphs of proportional relationships
- Interpret constant of proportionality in graphs

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# Writing proportional equations from tables

Writing an equation to describe the relationship between the number of scoops in an ice cream cone and the price. Created by Sal Khan.

## Want to join the conversation?

- since change x/ change y=slope, then if the line doesn't intersect zero then what r u supposed to do?(6 votes)
- If it doesn't intersect zero, then it's not a proportional relationship.(6 votes)

- Does the bigger number always goes on top or can it go on the bottom?(5 votes)
- Big numbers don't always go on top. They can also go on the bottom. Just remember that y always go on top and x goes on the bottom. No matter how big or small a number is, this rule still applies. Most of the time, the small numbers go on the bottom.(2 votes)

- So when I went to the practice: writing proportional equations, it said "A unicorn daycare center requires there to be 2 supervisors for every 18 unicorns. Write an equation that shows the relationship between the number of supervisors (n) and the number of unicorns (u). I put n=9u because n= 1 supervisor and 9u= 9 unicorns. It said i was wrong so i looked through the hints to see where i messed up and it says the answer is u=9n which means it takes 9 supervisors to care for 1 unicorn. My question is whether I misunderstood the work, or if the answer itself is wrong.(7 votes)
- This is not as hard as you make it(5 votes)
- Can anyone explain how this guy just converts 1 and 3/4 into 7/4. I was following along well until he just starts converting expressions instead of actually explaining how it relates to the problem rather just saying 1 and 3/4 is equal to 7/4.(2 votes)
- You have to get a common denominator which is 4. So 1= 4/4, then add 4/4 + 3/4 = 7/4(4 votes)

- How do you know when the answer to the problem is in fraction form(2 votes)
- If it is a fraction that cannot be simplified and when it is changed into a decimal, and it is very long, then it was meant to be shown as a fraction.(3 votes)

- what is 14/9 and and x=2(3 votes)
- At2:00he says that Y=7/4x

That's wrong! X=7/4 Y. Why did he switch them around?

In the equation shows clearly that when X=1 Y=7/4 You can't just switch the letters like that when they represent different things!(2 votes)- No, Sal didn't switch them around. He simply transposed x to the other side which resulted in the equation Y = 7/4 X. By the way, even if Sal made a mistake, you could have said it in subtler tone in the clarifications page of the video :)(2 votes)

- How do we write a more complex equation?(2 votes)
- Well, in this example, that is as hard as it can get. However a more complex equation would have to come from a more complex problem. :) The equation: y=7/4x or x=4/7y is our answer.(2 votes)

- Can you do proportional equations with negative numbers? Why or why not?(2 votes)
- Yes, you can.This is possible because uhhhh I really am not sure how to explain this so I try to clarify using a example. Let say you start with 500$(M) on monday then you spend 50$ every day.That would be a proportional relationship of which the equation would be M x -10% or M x -1/10.That is the best I can explain it since I am only in 7th grade.So I hope this helps.(2 votes)

## Video transcript

I scream, you scream, we
all scream for ice cream. The following table
describes the relationship between the number of
scoops in an ice cream cone, represented by x. So this is the number of
scoops in an ice cream cone. So that's x, and the price of
the cone, represented by y. I'll do y in purple. Write the equation that
describes this relationship. So let's see. When x is 0, y is 0. When x is 1, y is 1 and 3/4. So let me write this as
an improper fraction, just so I can
visualize it better. So this is 4/4 plus 3/4,
which is equal to 7/4. When x is 2, y is 3 and 1/2. So let me see if
I can write this in a little bit
of a clearer way. So 2 times 3 is 6,
plus 1 is 7, so this is 7/2-- which is the
same thing as 14 over 4. And then here we
have, when x is 3, y is equal to-- so 5 and
1/4-- if I would write it as an improper fraction-- 4
times 5 is 20, plus 1 is 21. So this is equal to 21 over 4. And then finally, if we were to
write this as something over 4, this is equal to 28 over 4. 7 is the same
thing as 28 over 4. So you see that this is a
proportional relationship. The ratio between y and x. So let me write this. The ratio between y and
x is always equal to 7/4. Notice here, y is 7/4 of x. 7/4-- it's a bigger number. Or you could say 1 and 3/4 of x. So let me make that clear. So y over x is equal to 7/4. Or, we can say that
y is always 7/4 of x. We can multiply both
sides by x, if we like. So if we multiply
both sides by x, we get y is equal
to 7/4 times x. And you see it here. When x is 4, 7/4 times 4 is 7. When x is 0, y is 0. When x is 3, 7/4
times 3 is 21 over 4, which is the same
thing as 5 and 1/4. So there we go. And let me input
it, just to make sure we can input it right. So y is equal to 7/4 x. We would just write y
is equal to 7/4 times x. And let's check our answer. And we got it right.