ANSWER
No
EXPLANATION
To see if this table represents a linear function, we have to find the slope - also called the average rate of change,
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]We can find it using the first two points in the table, (-2, -7) and (-1, 1),
[tex]m=\frac{1-(-7)}{-1-(-2)}=\frac{1+7}{-1+2}=\frac{8}{1}=8[/tex]Let's assume that this is a linear function. Then, the equation would be,
[tex]y=8x+b[/tex]Use the first point in the table to find the y-intercept, b,
[tex]\begin{gathered} -7=8\cdot(-2)+b \\ -7=-16+b\text{ }\Rightarrow\text{ }b=16-7=9 \end{gathered}[/tex]So, we have the equation,
[tex]y=8x+9[/tex]Now, we have to check if all the points in the table satisfy this equation. If they do, then the table represents a linear function and this is the equation,
[tex]\begin{gathered} -7=8(-2)+9 \\ -7=-16+9 \\ -7=-7\text{ }\Rightarrow\text{ }true \end{gathered}[/tex][tex]\begin{gathered} 1=8(-1)+9 \\ 1=-8+9 \\ 1=1\text{ }\Rightarrow\text{ }true \end{gathered}[/tex][tex]\begin{gathered} 8=8\cdot0+9 \\ 8=8\text{ }\Rightarrow\text{ }false \end{gathered}[/tex]The third point in the table does not satisfy the linear equation, but all the other points do.
Hence, this table does not represent a linear function.