Final answer:
The slope of a line perpendicular to 9x + 3y = 36 is 1/3.
Step-by-step explanation:
The given line equation is 9x + 3y = 36.
To find the slope of a line perpendicular to this line, we first need to find the slope of the given line. We can rewrite the equation in slope-intercept form y = mx + b, where m is the slope. Rearranging the equation, we get 3y = -9x + 36 and dividing both sides by 3, we get y = -3x + 12.
The slope of the given line is m = -3. The slope of a line perpendicular to this line will be the negative reciprocal of -3, which is 1/3.