Final answer:
The line with a slope of -8 passing through points (7, n) and (8, -3) can be analyzed using the slope formula. Setting up the equation, solving for (n), and simplifying, we find (n = 5). Hence, the value of (n) is 5 for the given line.
Step-by-step explanation:
To find n, we can use the concept that slope is the ratio of the change in y (vertical change) to the change in x (horizontal change) between two points on a line. In mathematical terms, slope (m) is represented by (y2 - y1) / (x2 - x1). Given the slope m = -8 and points (8, -3) and (7, n), we apply the formula: -8 = (n - (-3)) / (7 - 8). Simplifying the right side, we have -8 = (n + 3) / -1. Multiplying both sides by -1 to isolate n, we get 8 = n + 3. Subtracting 3 from both sides gives us: n = 8 - 3. Thus: n = 5. Therefore, the value of n for the given line with a slope of -8 is 5.