To write the equation in slope-intercept form (y = mx + b), we start with the slope (m) and a point (x₁, y₁) that the line passes through.
Given:
- Slope (m) = \(\frac{1}{3}\)
- Point (-6, 0) (x₁ = -6, y₁ = 0)
We can use the point-slope form of the equation of a line, which is:
\[ y - y₁ = m(x - x₁) \]
Substituting the values:
\[ y - 0 = \frac{1}{3}(x - (-6)) \]
This simplifies to:
\[ y = \frac{1}{3}(x + 6) \]
Distributing \(\frac{1}{3}\):
\[ y = \frac{1}{3}x + \frac{6}{3} \]
\[ y = \frac{1}{3}x + 2 \]
Thus, the equation of the line in slope-intercept form is:
\[ y = \frac{1}{3}x + 2 \]
The correct choice from your options is:
y = one-third x + 2.