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Proportional Relationships There are three ways to represent proportional relationships: table, graph and an equation. Constant of Proportionality: Equation ð¦ = ð ð¥ y= kx k is the constant of proportionality. Also known as a unit rate or unit price. It is comparing a quantity to one single unit of another quantity. y is the dependent variable (output) x is the independent variable (input) Table Graph A table is in proportion if you get a constant of proportionality when you divide the two numbers. A graph is proportional if it is a straight line and goes through the origin. X (input) Y (output) 0 0 1 3 2 6 3 9 By manipulating the formula to find the constant of proportionality, you get the equation. ð¦ = ð ð¥ (ð¥) ð¦ = ð(ð¥) ð¥ ð¦ = ðð¥ A table shows multiple equivalent ratios. To test to see if the table is proportional, you divide y by x and see if they are all equal. If they are all equal, then the number is the constant of proportionality. With the table being arranged as a comparison of x to y, it lends itself to creating a graph. A graph has to have two characteristics of being a straight line and goes through the origin. Both of these characteristics need to be on the graph. With a graph of the proportional relationship you can see the unit rate at (1,r) r is the same as the constant of proportionality. In the above example, you can see how the graph is straight, includes the origin (0,0) and has a constant of proportionality 3 by looking at (1,3).