Answer:
Table 4 represents the linear function.
Step-by-step explanation:
For table 1.
y = mx + c
m = (y-y')/(x-x') = (2-1)/1-0 = 1
y = x +c
Since point(2, 4) lies on the the line
4 = 2 + c
c = 2
y = x + 2
If third point(3, 8) passes through the line then it's a linear function.
8 = 3 + 2 = 5
which is not true therefore its nor linear.
For table 2
y = mx + c
passes through origin (0,0)
so c =0
m = (0-1)/(0-1) =1
y = x is the equation
But points 2 and 3 of the table don't follow the equation so function is non linear.
For table 3
y = mx + c
passes through (0,0)
so c =0
m = (1-0)/(1-0) = 1
y = x will the equation but points 3 and 4 don't pass through this line so function is non linear.
For 4th table
y = mx + c
m = (1-3)/(0-1) = 2
passe through (2, 5)
5 = 2.2 + c
c = 1
y = 2x + 1
since Fourth point (3, 7) satisfy the function.
7 = 3.2 + 1 = 7
Therefore this table represents a linear function.
