Final answer:
The value of n that makes the line perpendicular to y = -1/5x pass through the points (n, -12) and (4, 8) is n = 0.
Step-by-step explanation:
To find the value of n so that the line perpendicular to y = -1/5x passes through the points (n, -12) and (4, 8), we can determine the slope of the given line and then find the negative reciprocal to get the slope of the perpendicular line.
The given line has a slope of -1/5, so the perpendicular line will have a slope of 5.
Using the slope-intercept form of a line, y = mx + b, we can substitute the coordinates of one of the given points to find the y-intercept, b. Let's use the point (4, 8):
8 = 5(4) + b
b = 8 - 20
b = -12
Therefore, the equation of the perpendicular line is y = 5x - 12.
To find the value of n that makes the line pass through the point (n, -12), we substitute -12 for y and solve for n:
-12 = 5(n) - 12
0 = 5(n)
n = 0
Therefore, the value of n that makes the line perpendicular to y = -1/5x pass through the points (n, -12) and (4, 8) is n = 0.