Find the slope of the line of the points a=(-4,6) and b=(5,-4).

Here is the solution for finding the slope of the line for each pair of points.

The formula for the slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

a) For the points $(-4, 6)$ and $(4, 3)$

Step 1: Assign the coordinates. Let $(x_1, y_1) = (-4, 6)$ Let $(x_2, y_2) = (4, 3)$

Step 2: Substitute the values into the slope formula. $m = \frac{3 - 6}{4 - (-4)}$

Step 3: Simplify the expression. $m = \frac{-3}{4 + 4}$ $m = \frac{-3}{8}$

The slope for part a) is $\boxed{-\frac{3}{8}}$.

b) For the points $(5, 4)$ and $(6, -4)$

Step 1: Assign the coordinates. Let $(x_1, y_1) = (5, 4)$ Let $(x_2, y_2) = (6, -4)$

Step 2: Substitute the values into the slope formula. $m = \frac{-4 - 4}{6 - 5}$

Step 3: Simplify the expression. $m = \frac{-8}{1}$ $m = -8$

The slope for part b) is $\boxed{-8}$.