Writing proportional equations from tables
About this video
Sal uses a table of ice cream scoops (x) and cone prices (y) to write an equation. He rewrites each price as an improper fraction over 4, sees that y/x is always 7/4, and writes y = 7/4 x, then checks it against the table.
You'll be able to
- rewrite mixed numbers as improper fractions to compare values in a table.
- find the constant ratio y/x in a table of fractions.
- write an equation y = kx from a table and check it with values from the table.
Key words
- improper fraction
- A fraction whose top number is bigger than its bottom number, like 7/4.
- proportional relationship
- A relationship where y/x is always the same number.
- ratio
- A comparison of two numbers found by dividing one by the other.
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.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.