Let's start by analyzing the given equation and converting it into a more usable form.

The equation is:

$y - 2 = \frac{1}{3}(x + 5)$

Step 1: Simplify the equation

Distribute the $\frac{1}{3}$ on the right side:

$y - 2 = \frac{1}{3}x + \frac{5}{3}$

Step 2: Solve for $y$

Add 2 to both sides to isolate $y$:

$y = \frac{1}{3}x + \frac{5}{3} + 2$

Now, convert $2$ to $\frac{6}{3}$ to add it to $\frac{5}{3}$:

$y = \frac{1}{3}x + \frac{5}{3} + \frac{6}{3}$

$y = \frac{1}{3}x + \frac{11}{3}$

So, the equation of the line is:

$y = \frac{1}{3}x + \frac{11}{3}$

Step 3: Graph the line

To graph this, let's identify the slope and y-intercept:

• Slope: $\frac{1}{3}$ (which means for every 3 units you move horizontally, the line moves 1 unit up).
• Y-intercept: $\frac{11}{3}$ or approximately 3.67.

Plotting:

1. Start at the y-intercept $\left(0, \frac{11}{3}\right)$, which is roughly $(0, 3.67)$.
2. From there, use the slope $\frac{1}{3}$ to move 3 units to the right and 1 unit up to plot the next point.
3. Repeat the process in both directions to complete the line.

Would you like me to generate the graph for you?