Which table represents a linear function?

The  table which represents a linear function is:

Last table.

        x         y

        1         -5

        2         0

        3         5

        4         10

We know that a function is linear if the rate of change is constant.

i.e. the ratio of difference in y value to the corresponding difference in x value is constant.

i.e. for two values (x,y) and (x',y') the rate of change is given by:

In each of the tables we observe that the difference in x-value is constant i.e. 1.

since, 2-1=1

3-2=1

and 4-3=1

Now, the function will be linear for which the difference in the y-value is constant.

a)

        x       y

        1       5

        2       9

        3       5

        4       9      

The difference in the y-value is as follows:

9-5=4

5-9= -4

9-5= 4

Since, the difference is not constant.

Hence, the function is not linear.

b)

        x       y

        1       -5

        2       10

        3       -15

        4        20

 The difference in the y-value is as follows:

10-(-5)=15

-15-10= -25  

20-(-15)=35

Hence, the function is not linear ; since the difference in the y-value is not constant.

c)

        x         y

        1         5

        2        10

        3        20

        4        40

 The difference in the y-value is as follows:

10-5=5

20-10=10

40-20=20

Since, the difference in the y-value is not constant.

Hence, the function is not linear.

d)

        x         y

        1         -5

        2         0

        3         5

        4         10

 The difference in the y-value is as follows:

0-(-5)=5

5-0=5

10-5=5

Since, the difference in the y-value is constant.

Hence, the function is linear.

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step-by-step explanation:

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