The given equation is $y = x + \frac{\sqrt{3}}{3}$, and you are asked to find the angle that this line makes with the $Ox$ axis (the x-axis).

Step-by-step solution:

1. General form of the line equation: The general form of a line is $y = mx + b$, where $m$ is the slope of the line.

2. Extract the slope: In this case, $m = 1$, since the equation can be rewritten as $y = 1 \cdot x + \frac{\sqrt{3}}{3}$.

3. Relation between slope and angle: The angle $\theta$ that the line makes with the x-axis is related to the slope by the formula: $\tan(\theta) = m$ So in this case: $\tan(\theta) = 1$

4. Find the angle $\theta$: To find the angle, take the inverse tangent (arctangent) of both sides: $\theta = \tan^{-1}(1) = \frac{\pi}{4}$

Thus, the correct answer is e. $\frac{\pi}{4}$.

Would you like further details on this? Here are some additional questions to expand your understanding:

1. How do you convert between degrees and radians?
2. What is the meaning of the slope $m$ in a linear equation?
3. How do we derive the formula $\tan(\theta) = m$ for the slope?
4. What does the y-intercept $\frac{\sqrt{3}}{3}$ represent geometrically?
5. How would the angle change if the slope $m$ was greater or less than 1?

Tip: Always remember that the slope determines the steepness and direction of a line, and its relationship to the angle with the x-axis can be crucial in many geometric problems!