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.
We are given a line with a slope of -3, and we want to find the line perpendicular to this line. The slope of the perpendicular line can be found using the formula:
$$\text{slope}_{\text{perpendicular}} = -\frac{1}{\text{slope}} = -\frac{1}{-3} = \frac{1}{3}$$
Now that we have the slope of the perpendicular line, we can use the point-slope form of the line to find the equation. The point-slope form of a line is given by:
$$y - y_1 = m(x - x_1)$$
where $(x_1, y_1)$ is a point on the line and $m$ is the slope of the line. Plugging in the given point $(6, 1)$ and the slope $\frac{1}{3}$, we have:
$$y - 1 = \frac{1}{3}(x - 6)$$
Therefore, the point-slope form of the line that passes through $(6, 1)$ and is perpendicular to a line with a slope of -3 is $y - 1 = \frac{1}{3}(x - 6)$.