SOLUTION
We are asked which of the following tables have the same slope as the equation
[tex]y=-\frac{5}{8}x+4[/tex]
From the equation of a line
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope and b is the intercept on the y-axis} \end{gathered}[/tex]
Comparing this to the equation given, we can see that the slope m is
[tex]-\frac{5}{8}[/tex]
Now, we will use the formula for slope to check which one of the tables has the same slope as that on the equation
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]
Checking for table F, the slope is
[tex]\begin{gathered} m=\frac{-12-(-4)}{-3-(-1)_{}} \\ =\frac{-12+4}{-3+1} \\ =\frac{-8}{-2} \\ =4 \end{gathered}[/tex]
Hence, it is not table F.
Checking for table H, the slope is
[tex]\begin{gathered} m=\frac{6.5-2.75}{-4-2} \\ =\frac{3.75}{-6} \\ =-\frac{5}{8} \end{gathered}[/tex]
Hence, the answer is table H
