Question

These two equations represent a proportionality relationship.

3.75 = 1.25(3)

4.6875 = 1.25(3.75)

What is the constant of proportionality of the relationship represented in these equations?

Answer 1

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These two equations represent a proportionality relationship.

These two equations represent a proportionality relationship.3.75 = 1.25(3)

These two equations represent a proportionality relationship.3.75 = 1.25(3)4.6875 = 1.25(3.75)

These two equations represent a proportionality relationship.3.75 = 1.25(3)4.6875 = 1.25(3.75)What is the constant of proportionality of the relationship represented in these equations?

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The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other. Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k.

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If the relationship between two quantities is a proportional relationship, this relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate. For each point (x, y) on the graph, ž is equal to k, where k is the unit rate. The point (1, k) is a point on the graph.

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Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".

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Students calculate the rate of change also know as the constant of proportionality (k = y/x) which is the constant ratio between two proportional quantities y/x denoted by the symbol k which may be a positive rational number. The x value is directly proportional to the y value such as in the equation y = kx.

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This equation demonstrates direct proportionality, as we have the form #y=kx# where #k# is the constant of proportionality. Looking at the equation, #k=2/3# is our constant of proportionality because #2/3# is the constant number we multiply #x# by.