Linear or nonlinear tables?

Table 1 and Table 2 are linear tables while table 3 is a non-linear table.

Step-by-step explanation:

Step 1; If y's value is dependent on the value of x, it is a linear relationship i.e. as the value of x varies, y also varies correspondingly. So x is independent while y is dependent on x i.e. the value of y depends on the value of x. We need to determine if there is a linear relationship between the values of x and y in the given tables.

Step 2; In table 1, the values of y are squares of the values of x i.e. 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25. So the relationship is y = x². So table 1 is a linear table i.e. values which exist in a linear relationship.

Step 3; In table 2, the values of y are obtained by summing two times the value of x and 4.

when x = 1, y = 2(1) + 4 = 6,

when x = 2, y = 2(2) + 4 = 8,

when x = 3, y = 2(3) + 4 = 10,

when x = 4, y = 2(4) + 4 = 12,

when x = 5, y = 2(5) + 4 = 14.

So y = 2x + 4, so table 2 is also a linear table.

Step 4; There is no relationship between the values of y and x. For the negative values of x, y = -x while for positive values of x, y = x, there is no constant relationship between the values of y and x. So table 3 is a non-linear table.

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