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# Writing proportional equations

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

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.