Final answer:
To determine the value of p if a line with a slope of 5 passes through the points (10,15) and (16,p), we can use the formula for the slope of a line.
Step-by-step explanation:
To determine the value of p, we can use the formula for the slope of a line, which is given by:
m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
Using the points (10,15) and (16,p), we can substitute the values into the formula:
5 = (p - 15)/(16 - 10)
Simplifying the equation gives:
5 = (p - 15)/6
Multiplying both sides of the equation by 6 gives:
30 = p - 15
Adding 15 to both sides of the equation gives:
p = 45