Write the point-slope form of the line that passes through (6, 1) and is perpendicular to a line with a slope of -3. Include all of your work in your final answer. Type your answer in the box provided to submit your solution.
The slope of the line perpendicular to a line with a slope of -3 is the negative reciprocal of -3, which is $\frac{1}{3}$. So the line through $(6,1)$ has slope $\frac{1}{3}$. Using the point-slope formula, an equation for this line is \[y - 1 = \frac{1}{3}(x-6).\] Multiplying both sides by 3 gives $3y - 3 = x - 6$. Adding 6 to both sides of the equation gives $x - 3y = 3$. Thus, an equation for the line is $\boxed{x - 3y = 3}.$
