Final answer:
To find the value of p in the line that includes the points (-5, 9) and (3, p) with a slope of 7/4, we can use the slope formula. By setting up and solving an equation, we find that p is equal to 95/7 or 13.57.
Step-by-step explanation:
To find the value of p, we need to use the slope formula. The slope formula is given by m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Using the given points (-5, 9) and (3, p), and the slope of 7/4, we can set up the equation:
7/4 = (p - 9) / (3 - (-5))
To solve for p, we can cross multiply:
7(p - 9) = 4(3 - (-5))
Then, we simplify the equation and solve for p:
7p - 63 = 4(8)
7p - 63 = 32
7p = 32 + 63
7p = 95
p = 95/7
Therefore, the value of p is 95/7 or 13.57.