Calculate Slope of Linear Function: Points A(2,10) to B(-5,-4)

To find the slope of the graph of the linear function passing through points $A(2,10)$ and $B(-5,-4)$, we use the slope formula:

The slope formula is given by:

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

Substitute $(x_1, y_1) = (2, 10)$ and $(x_2, y_2) = (-5, -4)$:

$m = \frac{-4 - 10}{-5 - 2}$

Calculate the differences:

$y_2 - y_1 = -4 - 10 = -14$

$x_2 - x_1 = -5 - 2 = -7$

Substitute these into the slope formula:

$m = \frac{-14}{-7}$

Simplify:

$m = \frac{-14}{-7} = 2$

Therefore, the slope of the graph is $2$.