Calculate Slope Between Points A(1,7) and D(8,2): Linear Function Analysis

To find the slope of the linear function passing through the points $A(1,7)$ and $D(8,2)$, we will use the formula for the slope between two points:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Let us assign the coordinates $(x_1, y_1) = (1, 7)$ and $(x_2, y_2) = (8, 2)$.

Substitute these values into the slope formula:

$m = \frac{2 - 7}{8 - 1}$

Calculate the differences in the numerator and the denominator:

$m = \frac{-5}{7}$

Therefore, the slope of the line passing through points $A(1,7)$ and $D(8,2)$ is $-\frac{5}{7}$.

In conclusion, the correct answer is $-\frac{5}{7}$.