Final answer:
The slope of a line perpendicular to the line with the equation x - 2y = 14 is -2 because perpendicular slopes are negative reciprocals.
Step-by-step explanation:
To find the slope of a line perpendicular to another line, you must first know the slope of the original line.
The equation given is x - 2y = 14, which we can rewrite in slope-intercept form (y = mx + b) to find its slope.
By adding 2y to both sides and subtracting 14 from both sides, we get 2y = x - 14.
Then, we divide both sides by 2 to solve for y, resulting in y = 1/2x - 7. Thus, the slope (m) of this line is 1/2.
Perpendicular lines have slopes that are negative reciprocals of each other.
So, if the slope of the original line is 1/2, the slope of a line perpendicular to it would be the negative reciprocal of 1/2, which is -2 (flipping the fraction and changing the sign).
All lines that are perpendicular to the original line will have this slope of -2, regardless of their y-intercept.