Let's solve this step by step to help you graph the line described by the equation:

Equation:
$y - 5 = -\frac{1}{3}(x + 6)$

Step 1: Rewrite the equation in slope-intercept form ($y = mx + b$).

We start by simplifying the equation.

1. Distribute $-\frac{1}{3}$ to $x + 6$: $y - 5 = -\frac{1}{3}x - 2$

2. Add 5 to both sides to isolate $y$: $y = -\frac{1}{3}x + 3$

Step 2: Identify the slope ($m$) and y-intercept ($b$).

• The slope ($m$) is $-\frac{1}{3}$. This means the line decreases by 1 unit vertically for every 3 units it moves horizontally.
• The y-intercept ($b$) is 3. This means the line crosses the y-axis at the point $(0, 3)$.

Step 3: Plot key points.

1. Start with the y-intercept: Plot the point $(0, 3)$.
2. Use the slope to find another point:
   Starting at $(0, 3)$, use the slope $-\frac{1}{3}$:
   • Move down 1 unit (negative slope) and right 3 units to find the point $(3, 2)$.
3. Another point: From $(3, 2)$, repeat the slope:
   • Move down 1 unit and right 3 units to find the point $(6, 1)$.

Step 4: Graph the line.

1. Plot the points $(0, 3)$, $(3, 2)$, and $(6, 1)$ on the graph.
2. Draw a straight line through these points.

Would you like me to verify further steps, or provide more explanation about graphing lines?

Related Questions:

1. How do you find the slope and y-intercept from a linear equation?
2. What are alternative methods to graph linear equations without converting to slope-intercept form?
3. How can you verify that a point lies on a given line?
4. What does a positive vs. negative slope look like on a graph?
5. How would you graph a vertical or horizontal line?

Tip: Always double-check your calculations for slope and y-intercept to avoid errors when plotting points.