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Lesson 6: Equations of proportional relationships

# 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?

• when x = 1 he wrote 7/4, then when x=2 he wrote 14/4, how is this the same?
• One thing he forgets to make clear in this video, even though the constant is 7/4, is to remember each line is going up by one multiplier (in the left column).

so its 1 x 7/4 and then the next row is 2 x 7/4 (14/4) and then 3x 7/4 (21/4) he explains it as if each value in the last column is 7/4 which is not true. The constant of each row is 7/4. His wording is a bit off that's why it doesn't make sense 100% to everyone.

He says it like each value in the right column is equivalent to 7/4 which is not true at all (we can clearly see that 28/4 is not equal to 7/4 it is 4 times greater). He means the constant of that row is 7/4, but just forgot to word it like that.
• Why did Sal sound so depressed when he said: "I scream. you scream. we all scream for ice cream!"?
• haha idk,he didn't sound that way to me at first, but now i hear it...
• How does he make it look so easy and I am over here still struggling 😭
• he makes it look so simple im still confused
• since change x/ change y=slope, then if the line doesn't intersect zero then what r u supposed to do?
• If it doesn't intersect zero, then it's not a proportional relationship.
• Does the bigger number always goes on top or can it go on the bottom?
• 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.
• I scream out of pure frustration and anger
• me too
• 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.
• The hint answer is right because it says that the number of unicorns(u) is equal to 9 times the numbers of supervisors(n), so the equation is indeed u=9n. That is because when it is 1 supervisor(n) the number of unicorns is 9 * 1(9n) in this case 1 which is 9 unicorns, and if the number of supervisors is 2 the number of unicorns is 9 * 2(9n) so the result of 9n will always be the number of unicorns.
• How do you know when the answer to the problem is in fraction form
• 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.
• 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.
• You have to get a common denominator which is 4. So 1= 4/4, then add 4/4 + 3/4 = 7/4
• This is not as hard as you make it

## 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.