Calculate the Slope: Linear Function through Points (0,7) and (-4,-9)

To find the slope ($m$) of the line passing through the points $A(0,7)$ and $B(-4,-9)$, we apply the slope formula:

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

First, assign the coordinates to the two points:

• $(x_1, y_1) = (0, 7)$
• $(x_2, y_2) = (-4, -9)$

Next, substitute these into the slope formula:

$m = \frac{-9 - 7}{-4 - 0}$

Simplify the expression:

$m = \frac{-16}{-4}$

The negative signs in the numerator and denominator cancel out:

$m = \frac{16}{4}$

Finally, divide to find the slope:

$m = 4$

Therefore, the slope of the line passing through points $A(0,7)$ and $B(-4,-9)$ is $4$.