the table that represents a linear relatiponship is option C
Explanation:
For the table to show linear relationship, the slope at any given two points should be equal.
slope = change iiny/change in x
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]
Using the first two points for the x and y values in the table:
a) slope = (5-2)/(2-1) = (8-5)/(4-2)
slope = 3/1 = 3/2
slope = 3 = 3/2
The slopes are not equal for the points used
b) slope = (5-2)/(1-(-4)) = (8-5)/(2-1)
slope = 3/(1+4) = 3/1
slope = 3/5 = 3/1
The slopes are not equal for the points used
c) slope = (5-2)/(-2-(-4)) = (8-5)/(0-(-2))
slope = 3/(-2+4) = 3/(0+2)
slope = 3/2 = 3/2
The slopes are equal for the points used
d) slope = (5-2)/(0-(-1)) = (8-5)/(2-0)
slope = 3/(0+1) = 3/2
slope = 3/1 = 3/2
The slopes are not equal for the points used
Hence, the table that represents a linear relatiponship is option C
