Final answer:
The constant of proportionality defines the linear relationship between two directly proportional quantities and can be found by dividing y by x from a table of values.
Step-by-step explanation:
The constant of proportionality is a number that defines the linear relationship between two directly proportional quantities. When two quantities are directly proportional, the ratio between them always remains constant. This can be represented mathematically by the equation y = kx, where y is one quantity, x is the other quantity, and k is the constant of proportionality. This constant can be found by dividing the y value by the x value when given a table of two directly proportional variables.
To find the constant of proportionality for each table, you would take any given value of y (such as the number of shoes or distance traveled) and divide it by its corresponding x value. As an example, if the table indicated that 4 shoes are associated with 8 meters traveled, the constant of proportionality (k) would be calculated as k = y / x = 8 / 4 = 2. Therefore, the constant of proportionality for this table would be 2, meaning that for every additional shoe, the distance traveled increases by 2 meters.
The complete question is: The tables show the proportional relationship between two quantities. Write the constant of proportionality for each table.
(3) Number of shoes | Distance traveled
(A) The constant of proportionality is ___
(B) The constant of proportionality is ___
(C) The constant of proportionality is ___