Final answer:
To find the value of p for the given line with a slope of -9, we used the slope formula resulting in p being equal to 5.
Step-by-step explanation:
The student asked to find the value of p for a line that has a slope of -9 and includes the points (4,p) and (5, –4).
To find p, we use the slope formula which is (y2 - y1) / (x2 - x1).
Since the slope is given as -9, we set up our equation as: (-4 - p) / (5 - 4) = -9.
Simplifying gives us -4 - p = -9.
Solving for p, we add 4 to both sides resulting in p = 5.