To determine the graph that features the point (-1, -2) and a slope of \( \frac{1}{3} \), we can use the point-slope form of a linear equation. The point-slope form is given by:
\[ y - y_1 = m(x - x_1) \]
In this equation:
- \( (x_1, y_1) \) is the point \((-1, -2)\),
- \( m \) is the slope, which is \( \frac{1}{3} \).
Substituting in the values, we get:
\[ y - (-2) = \frac{1}{3}(x - (-1)) \]
Simplifying this gives:
\[ y + 2 = \frac{1}{3}(x + 1) \]
Which leads to:
\[ y + 2 = \frac{1}{3}x + \frac{1}{3} \]
Subtracting 2 from both sides:
\[ y = \frac{1}{3}x + \frac{1}{3} - 2 \]
\[ y = \frac{1}{3}x - \frac{5}{3} \]
Now that we have the equation of the line, we can check the graph you have for the following characteristics:
- It must pass through the point (-1, -2).
- The slope of the line must be \( \frac{1}{3} \).
If you provide the graphs or their specifics, I can help you identify the correct one.