Step 1 :The slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Step 2 :In this case, the two points are \((-5,2)\) and \((6,3)\). So, we can substitute these values into the formula to find the slope.
Step 3 :After executing this calculation, we get the slope of the line as approximately 0.09.
Step 4 :We can determine whether the line rises, falls, is horizontal, or is vertical based on the slope. If the slope is positive, the line rises; if the slope is negative, the line falls; if the slope is zero, the line is horizontal; if the slope is undefined (i.e., the denominator in the slope formula is zero), the line is vertical.
Step 5 :The slope of the line is approximately 0.09, which is a positive number. Therefore, the line rises from left to right.
Step 6 :Final Answer: The slope is \(\boxed{0.09}\). The line rises.