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I scream you scream we all scream for ice cream the following table describes the relationship between the number of scoops and an ice cream cone represented by X so this is the number of number of scoops in an ice cream cone so that's X and the price of the cone represented by Y of the 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 halves 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 to 5 right is 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 a 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 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 why did Y over X is equal to 7/4 or we can say that Y is always 7/4 of X we could multiply both sides by X if we like so if we multiply both sides by X we get Y is equal to is equal to 7/4 7/4 times X and you see it here when X is 4 7/4 times four is seven one zero when x is 0 Y is zero when X is 3 7 4 times 3 is 21 over 4 which is the same thing as five and one fourths 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 let me get my so we would just write we would just write Y is equal to 7 over 4 times X and let's check our answer and we got it right