Question - Determining the Equation of a Proportional Relationship
mathproportional relationshipconstant of proportionalityequation of proportionalitydetermining k value
Solution:
To find the equation of the form y = kx that represents the proportional relationship between x and y, we must first determine the constant of proportionality k by dividing the value of y by the value of x for any given point in the table. The constant of proportionality should be the same for any pair of x and y values listed, as long as the relationship is truly proportional.For example, take the first row where x is 18 and y is 153.k = y / x = 153 / 18 = 8.5Now we should check this value of k to see if it applies to the other rows. If the relationship is proportional, then all rows should have the same value of k.For the second row, with x as 24 and y as 204:k = y / x = 204 / 24 = 8.5For the third row, with x as 30 and y as 255:k = y / x = 255 / 30 = 8.5Since all rows give us the same k value, we can confirm that the relationship is proportional and the constant of proportionality k is 8.5.Therefore, the equation that represents the relationship is y = 8.5x.
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