Suppose the relationship between x and y is proportional. When x is 29, y is 275.5. Find the constant of proportionality of y to x. Use the constant of proportionality to find x when y is 408.5. Use pencil and paper. Explain how you can tell a relationship that is proportional from a relationship that is not proportional.

The constant of proportionality, k, when x is 29 and y is 275.5 is: 9.5
Using the constant of proportionality, k = 9.5, when y = 408.5, x will be: 43.
A proportional relationship can be modelled by the equation, y = kx while a non-proportional relationship cannot.

Note the following:

A relationship that is proportional can be modelled by the equation: y = kx
The k is the constant of proportionality or unit rate.

Thus:

If x and y are proportional, and x = 29 when y = 275.5,

Constant of proportionality (k) can be calculated by substituting the values of x and y into y = kx, and then solving for k.

275.5 = k29

275.5/29 = k

k = 9.5

Constant of proportionality, k, is: 9.5

Using the constant of proportionality, k = 9.5, to find x when y = 408.5, plug in the values of k and y into y = kx, then solve for x.

408.5 = 9.5x

408.5/9.5 = x

x = 43

In summary:

The constant of proportionality, k, when x is 29 and y is 275.5 is: 9.5
Using the constant of proportionality, k = 9.5, when y = 408.5, x will be: 43.
A proportional relationship can be modelled by the equation, y = kx while a non-proportional relationship cannot.

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