Final answer:
The value of p on the straight line defined by the points (-1,16), (3,8), and (p,78) is -32, which is obtained by calculating the consistent slope of -2 from the first two points and applying it across the entire line to solve for p.
Step-by-step explanation:
The value of p can be determined using the concept of the slope of a straight line. In this question, the points (-1,16), (3,8), and (p,78) lie on the same line. The slope of this line can be found by using any two points on the line. The slope is the ratio of the change in the y-coordinates to the change in the x-coordinates (rise over run).
For the points (-1,16) and (3,8), the slope (m) can be calculated as follows:
m = (y2 - y1) / (x2 - x1)
m = (8 - 16) / (3 - (-1))
m = (-8) / (4)
m = -2
The same slope must exist between the points (3,8) and (p,78). Using the slope formula again:
-2 = (78 - 8) / (p - 3)
-2 = 70 / (p - 3)
To find p, multiply both sides by (p - 3) and then divide both sides by -2:
70 = -2(p - 3)
70 = -2p + 6
64 = -2p
p = -32
Therefore, the value of p is -32.