Find the slope of a line perpendicular to the line whose equation is 3, x, plus, y, equals, 3x+y=8. Fully simplify your answer.
To find the slope of a line perpendicular to the given line, we first need to find the slope of the given line. The equation of the given line is 3x + y = 8, which can be rewritten in slope-intercept form (y = mx + b) by solving for y:
y = -3x + 8
The slope of the given line is -3.
Since the slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line, the slope of a line perpendicular to 3x + y = 8 is the negative reciprocal of -3.
The negative reciprocal of -3 is 1/3.
Therefore, the slope of a line perpendicular to 3x + y = 8 is 1/3.