Calculate Slope Between Points (0,4) and (-5,6): Coordinate-Based Problem

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information about the points.
• Step 2: Use the slope formula to find the slope.
• Step 3: Calculate and simplify.

Now, let's compute the slope:

Step 1: The points given are $(0, 4)$ and $(-5, 6)$.

Step 2: Apply the slope formula:

The slope $m$ is given by:

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

Substitute the known values:

$y_2 = 6, \; y_1 = 4, \; x_2 = -5, \; x_1 = 0$ $m = \frac{6 - 4}{-5 - 0} = \frac{2}{-5}$

Step 3: Simplify the expression:

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

Thus, the slope of the line passing through the points $(0, 4)$ and $(-5, 6)$ is $-\frac{2}{5}$.

Therefore, the solution to the problem is $-\frac{2}{5}$.