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To solve the problem, we need to find the equation of the tangent line to the graph of the function \( f(x) \) at the point where \( x = 0 \).

### Step-by-Step Solution:

1. **Determine the Point on the Graph:**
   The function value at \( x = 0 \) is given by \( f(0) = 2 \). Thus, the point on the graph is \( (0, 2) \).

2. **Find the Slope of the Tangent Line:**
   The slope of the tangent line is given by the derivative of the function at the point of tangency. We are given that \( f'(0) = -3 \). Therefore, the slope of the tangent line is \( -3 \).

3. **Formulate the Equation of the Tangent Line:**
   The equation of a line with slope \( m \) passing through a point \( (x_1, y_1) \) can be written as:
   \[
   y - y_1 = m(x - x_1)
   \]
   Substituting \( x_1 = 0 \), \( y_1 = 2 \), and \( m = -3 \), we get:
   \[
   y - 2 = -3(x - 0)
   \]
   Simplifying, we have:
   \[
   y - 2 = -3x
   \]
   or
   \[
   y = -3x + 2
   \]

4. **Match with the Given Options:**
   The equation can be rearranged to match the format of the options provided. In the format \( y - y_1 = m(x - x_1) \), it matches:
   \[
   y - 2 = -3(x - 0)
   \]

   This corresponds to the second option:
   \[
   \text{Option B: } y - 2 = -3(x - 0)
   \]

### Conclusion:
The correct answer is **Option B**: \( y - 2 = -3(x - 0) \).

Would you like a more detailed explanation or have any questions? 

Here are some related questions you might find useful:
1. How do you find the tangent line of a function at any point?
2. What does the derivative of a function tell us about its graph?
3. How can you determine concavity from the second derivative?
4. What is the geometric interpretation of the second derivative being zero at a point?
5. How does the point-slope form of a line differ from the slope-intercept form?

**Tip:** Remember that the slope of the tangent line to a curve at a point represents the instantaneous rate of change of the function at that point.

Suppose that the function f has a continuous second derivative for all x, and that f(0) = 2, f'(0) = -3, and f''(0) = 0. Write an equation of the line tangent to the graph of f at the point where x = 0.

Learn how to find the equation of the tangent line to the function f(x) at the point where x = 0. This problem covers key calculus concepts including the derivative and tangent lines, with a step-by-step solution. Suitable for high school students in grades 11-12 or those studying Calculus.

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