The problem is asking for the equation of a line in point-slope form given the slope $m = -\frac{1}{3}$ and a point on the line $(6, 3)$.

The point-slope form of the equation of a line is given by: $y - y_1 = m(x - x_1)$ where $m$ is the slope and $(x_1, y_1)$ is a point on the line.

Substituting the given values:

• $m = -\frac{1}{3}$
• $x_1 = 6$
• $y_1 = 3$

We plug these values into the point-slope form: $y - 3 = -\frac{1}{3}(x - 6)$

So the equation in point-slope form is: $y - 3 = -\frac{1}{3}(x - 6)$

Let me know if you'd like further details or have any questions!

Here are 5 related questions to extend this topic:

1. How can we convert this point-slope equation to slope-intercept form?
2. What is the equation of the line parallel to this one that passes through a different point?
3. How do you find the x- and y-intercepts of a line given in point-slope form?
4. How does the point-slope form relate to the distance between two points on the line?
5. What happens if the slope is zero or undefined?

Tip: Always use point-slope form when you know the slope and one point, as it is the quickest method to write a line equation!