Question

Plz help! Which table shows a linear function?

Answer 1

Answer: The second table shows the linear function.

Explanation:

The slope of linear function is same for all pair of points on line. It means the value of y changes in the same proportion of x. In linear function for each value of x there is unique value of y.

$\text{slope}=\frac{\text{change in y}}{\text{change in x}}$

The graph of a linear function is a straight line.

In first table, for x=-1 and x=1 the value of y is same, i.e., 2. So, this table does not represent a linear function.

In second table, for first two points the change in x is 4 then change in y is 8 it means the slope is,

$\text{slope}=\frac{8}{4} =2$

It means if x increases by 1 unit then value of y increased by 2 units and vice versa. This statement is true for all point of the table,therefore this table represent a linear function.

In third table, for first two points the change in x is 1 then change in y is 2 it means the slope is,

$\text{slope}=\frac{2}{1} =2$

It means if x increases by 1 unit then value of y increased by 2 units and vice versa. This statement is not true for all point of the table because for last two points change in x is 1 but the change in y is 7. So, this table does not represent a linear function.

In fourth table, for first two points the change in x is 1 then change in y is 7 it means the slope is,

$\text{slope}=\frac{7}{1} =7$

It means if x increases by 1 unit then value of y increased by 7 units and vice versa. This statement is not true for all point of the table because for next two points change in x is 1 but the change in y is 1. So, this table does not represent a linear function.

Therefore, only second table shows the linear function.

Answer 2

The second table. A linear function is a function where adding the same amount to x should add the same amount to y.

In table 2, you can see that adding 1 to x adds 2 to y. All the other tables describe non-linear functions.