Final answer:
The value of k is determined using the slope formula and is found to be 2.
Step-by-step explanation:
The value of k can be determined by using the slope formula, which is (y2 - y1) / (x2 - x1). We are given that the slope of the line is -1/4, and the points are (5, k) and (9, 1).
Using the slope formula:
-1/4 = (1 - k) / (9 - 5)
Multiplying both sides by 4 to eliminate the fraction:
-1 = 4 * (1 - k) / 4
-1 = 1 - k
Subtracting 1 from both sides gives us:
-2 = -k
Dividing both sides by -1 gives us the value of k:
k = 2