Answer:
From the above options, the only table that have the same slope as the given line in the equation (m=2) is Table C.
[tex]\begin{gathered} m=\frac{3-\mleft(-7\mright)}{4-(-1)} \\ m=\frac{10}{5} \\ m=2 \end{gathered}[/tex]Explanation:
Given the equation;
[tex]y=2x+1[/tex]The slope of the above line is;
[tex]m=2[/tex]From the given options, let us find the table that has the same slope as the above equation;
A.
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-8-7}{3-(-2)} \\ m=\frac{-15}{5} \\ m=-3 \end{gathered}[/tex]B.
[tex]\begin{gathered} m=\frac{4-2}{2-(-2)} \\ m=\frac{2}{4} \\ m=\frac{1}{2} \end{gathered}[/tex]C.
[tex]\begin{gathered} m=\frac{3-\mleft(-7\mright)}{4-(-1)} \\ m=\frac{10}{5} \\ m=2 \end{gathered}[/tex]D.
[tex]\begin{gathered} m=\frac{-1-2}{4-(-2)} \\ m=\frac{-3}{6} \\ m=-\frac{1}{2} \end{gathered}[/tex]From the above options, the only table that have the same slope as the given line (m=2) is Table C.
[tex]\begin{gathered} m=\frac{3-\mleft(-7\mright)}{4-(-1)} \\ m=\frac{10}{5} \\ m=2 \end{gathered}[/tex]