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.
The point-slope form of a line is given by
y - y₁ = m(x - x₁),
where (x₁, y₁) is a point on the line and m is the slope of the line.
Since the line we are looking for is perpendicular to a line with slope -3, the slope of our line will be the negative reciprocal of -3, which is 1/3.
Plugging in the given point (6, 1) into the point-slope form, we have:
y - 1 = (1/3)(x - 6).
Expanding, we get:
y - 1 = (1/3)x - 2.
Finally, rearranging the equation, we have:
y = (1/3)x - 1.