To find the equation of a line with a slope of \(\frac{1}{3}\) that passes through the point \((-2, 1)\), we can use the point-slope formula:
\[ y - y_1 = m(x - x_1) \]
where \(m\) is the slope, and \((x_1, y_1)\) is the point the line passes through. In this case, \(m = \frac{1}{3}\), \(x_1 = -2\), and \(y_1 = 1\).
Plugging these values into the formula gives:
\[ y - 1 = \frac{1}{3}(x + 2) \]
Now, simplify the equation:
\[ y - 1 = \frac{1}{3}x + \frac{2}{3} \]
Adding \(1\) (or \(\frac{3}{3}\)) to both sides results in:
\[ y = \frac{1}{3}x + \frac{2}{3} + \frac{3}{3} \] \[ y = \frac{1}{3}x + \frac{5}{3} \]
Therefore, the equation of the line is:
\[ y = \frac{1}{3}x + \frac{5}{3} \]
The correct answer is:
y = one-third x + five-thirds.