Find the slope of a line perpendicular to the line whose equation is x, plus, y, equals, 3x+y=3. Fully simplify your answer.
To find the slope of the line given by the equation 3x+y=3, we need to rewrite it in slope-intercept form y=mx+b, where m is the slope of the line.
Starting with the given equation:
3x+y=3
Rearranging to solve for y:
y = -3x + 3
Now we can see that the slope of the given line is -3.
Since the slope of a line perpendicular to a line with slope m is the negative reciprocal of m, the slope of the line perpendicular to the given line is:
Perpendicular slope = -1/(-3)
Perpendicular slope = 1/3
Therefore, the slope of a line perpendicular to the line whose equation is 3x+y=3 is 1/3.