Table 3 shows a proportional relationship between x and y as x/y is constant for the values in each row.
What do we mean by a proportional relationship between two quantities?
Proportional relationships are those in which the ratios of two variables are the same. Another way to think about them is that one variable is always a constant value time the other in a proportionate relationship. The "constant of proportionality" is the name given to this constant.
How do we solve the given question?
We are asked to tell which table from the given tables shows a proportional relationship between x and y.
We check each table for a proportional relationship between x and y.
Table 1:
x = 2 gives y = 4. x/y = 2/4 = 1/2.
x = 3 gives y = 6. x/y = 3/6 = 1/2.
x = 4 gives y = 9. x/y = 4/9.
Since x/y is not constant for all rows, x and y do not hold a proportional relationship.
Table 2:
x = 3 gives y = 4. x/y = 3/4.
x = 9 gives y = 16. x/y = 9/16.
x = 15 gives y = 20. x/y = 15/20 = 3/4.
Since x/y is not constant for all rows, x and y do not hold a proportional relationship.
Table 3:
x = 4 gives y = 12. x/y = 4/12 = 1/3.
x = 5 gives y = 15. x/y = 5/15 = 1/3.
x = 6 gives y = 18. x/y = 6/18 = 1/3.
Since x/y is constant for all rows, x and y do show a proportional relationship.
Table 4:
x = 1 gives y = 4. x/y = 1/4.
x = 2 gives y = 8. x/y = 2/8 = 1/4.
x = 3 gives y = 15. x/y = 3/15 = 1/5.
Since x/y is not constant for all rows, x and y do not hold a proportional relationship.
∴ Table 3 shows a proportional relationship between x and y as x/y is constant for the values in each row.
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