According to the provided graph, Finn needs proportionally more sugar based on the number of cakes. He would need 1 and 1/2 cups for 1 cake, 6 cups for 4 cakes, and 9 cups for 6 cakes, showing that the amount of sugar scales up directly with the number of cakes.
The question relates to proportional relationships in recipes which is a mathematical concept often studied in middle school. When Finn is baking cakes and the number of cups of sugar needed is proportional to the number of cakes, we are dealing with a ratio that should remain constant for all amounts.
Therefore, according to the graph provided, if Finn needs 1 and 1/2 cups of sugar for 1 cake, then for 4 cakes he would need 6 cups of sugar (since 1.5 x 4 = 6). It is not possible for Finn to need 112 cups of sugar for 1 cake as that would disagree with the provided proportional relationship. Similarly, Finn cannot need 1 cup of sugar for 112 cakes or 1 and 1/2 cakes because that would violate the constant ratio established by the graph. For 6 cakes, using the proportionality, he would need 1.5 x 6 = 9 cups of sugar, not 4 cups.