Final answer:
The slope of the line perpendicular to the line passing through the points (2,3) and (-6,27) is 3.
Step-by-step explanation:
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line. To find the slope of the line passing through the points (2,3) and (-6,27), we can use the formula:
Slope = (y2 - y1) / (x2 - x1)
Substituting the values, we get:
Slope = (27 - 3) / (-6 - 2) = 24 / -8 = -3
Therefore, the slope of the line perpendicular to the line passing through the given points is 3.