Final answer:
The value of p for the point (3, p) which lies on a line with a slope of 7/4 and passes through (-5, 9) is 23.
Step-by-step explanation:
The student is asked to find the value of p in the point (3, p) when a line passes through the points (-5, 9) and (3, p) and has a slope of 7/4. The slope of a line can be calculated using the formula slope = (y2 - y1) / (x2 - x1). Using the given points and slope, we can set up the equation 7/4 = (p - 9) / (3 - (-5)) and solve for p.
To find p, we multiply both sides by the denominator of the right side of the equation, which is 3 + 5 = 8, to get 7/4 * 8 = p - 9. Simplifying, we find that p - 9 = 14, and adding 9 to both sides gives us p = 14 + 9. Therefore, the value of p is 23.