To graph the line with slope $-\frac{1}{3}$ passing through the point $(3, 5)$, follow these steps:

Step-by-step solution:

1. Plot the given point $(3, 5)$:

   • Start by locating the point $(3, 5)$ on the graph. Move 3 units to the right on the x-axis and 5 units up on the y-axis.

2. Use the slope to find another point:

   • The slope $-\frac{1}{3}$ means that for every 3 units you move to the right (positive direction on the x-axis), you move 1 unit down (negative direction on the y-axis).
   • Starting from $(3, 5)$, move 3 units to the right (to $x = 6$) and 1 unit down (to $y = 4$). This gives the point $(6, 4)$.

3. Plot the second point $(6, 4)$.

4. Draw the line:

   • Draw a straight line passing through both points $(3, 5)$ and $(6, 4)$.

This will be the graph of the line with slope $-\frac{1}{3}$ passing through the point $(3, 5)$.

Would you like more details or have any questions?

Here are five related questions for further practice:

1. How would you graph a line with slope $\frac{2}{5}$ passing through point $(-2, -3)$?
2. What is the equation of the line with slope $4$ passing through $(1, -1)$?
3. How does the slope affect the steepness and direction of a line?
4. Can you determine the x-intercept of the line with slope $-\frac{1}{3}$ passing through $(3, 5)$?
5. What is the general equation of a line, and how can you find it using the slope and a point?

Tip: The slope formula, $\text{slope} = \frac{\Delta y}{\Delta x}$, can help you easily find other points on the line once you know one point.