Answer:
Table 3
Explanation:
A linear function has a constant slope.
To determine if the table represents a linear function, find the slope for two different pairs of points.
Table 1
Using the points (1,-2), (2,-6)
[tex]\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}=\frac{-6-(-2)}{2-1}=-6+2=-4[/tex]Using the points (2,-6), (3,-2)
[tex]\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}=\frac{-2-(-6)}{3-2}=-2+6=4[/tex]The slopes are not the same, thus, the function is not linear.
Table 3
Using the points (1,-2), (2,-10)
[tex]\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}=\frac{-10-(-2)}{2-1}=-10+2=-8[/tex]Using the points (2,-10), (3,-18)
[tex]\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}=\frac{-18-(-10)}{3-2}=-18+10=-8[/tex]The slopes are the same, thus, the function is linear.
Table 3 is the correct option.