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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. \( \frac{\pi}{4} \)**.

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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!

Duota tiesė y = x + sqrt(3)/3. Raskite šios tiesės kampą su Ox ašimi. Pasirinkite teisingą atsakymą: a) 0°, b) pi/6, c) pi/2, d) teisingo atsakymo nėra, e) pi/4, f) pi/3.

Learn how to calculate the angle between a line and the x-axis using the equation y = x + sqrt(3)/3. This problem involves key concepts in trigonometry and linear equations, suitable for high school students (Grades 9-12).

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