Final answer:
The value of n is 9.
Step-by-step explanation:
To find the value of n, we can use the formula for slope: m = (y2 - y1) / (x2 - x1).
Given that the slope is -9 and the points (n,7) and (10,-2), we can substitute the values into the formula to solve for n.
Using the points (10,-2) and (n,7):
-9 = (7 - (-2)) / (n - 10)
-9 = 9 / (n - 10)
Now we can cross multiply:
-9(n - 10) = 9
-9n + 90 = 9
-9n = -81
n = 9