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Determine the value of p if a line with a slope of 5 passes through the points (10,15) and (16,p).

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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

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