Answer:
The table that represent a linear function is:
x y
1 -2
2 -10
3 -18
4 -26
Step-by-step explanation:
We are asked to find which of the following table represent an linear function.
As the x-value is increasing by a constant value i.e. '1'.
Hence, for the function to be a linear function the value of y must also increase or decrease by the same constant.
This means the difference in the y-value from the preceding y-value must be same.
1)
x y Difference in y-value
1 -2
2 -5 -5-(-2)=-3
3 -9 -9-(-5)=-4
4 -14 -14-(-9)=-5
As the difference in y-value is different hence, the table does not represent a linear function.
2)
x y Difference in y-value
1 -2
2 -4 -4-(-2)=-2
3 -8 -8-(-4)=-4
4 -16 -16-(-8)=-8
As the difference in y-value is different hence, the table does not represent a linear function.
3)
x y Difference in y-value
1 -2
2 -6 -6-(-2)=-4
3 -2 -2-(-6)=4
4 -6 -6-(-2)=-4
As the difference in y-value is different hence, the table does not represent a linear function.
4)
x y Difference in y-value
1 -2
2 -10 -10-(-2)=-8
3 -18 -18-(-10)=-8
4 -26 -26-(-18)=-8
As, the difference in y-value is same.
Hence, the table represent a linear function.
