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The problem presents two graphs, \( g(x) \) and \( f(x) \), which appear to be related through a translation. We are asked to determine the value of \( a + b \), where \( T = \begin{pmatrix} a \\ b \end{pmatrix} \) represents the translation vector from the graph of \( g(x) \) to the graph of \( f(x) \).

### Step-by-Step Solution:

1. **Identify the equations of the graphs**:
   - The graph \( g(x) \) passes through points (0, 2) and (3, 0). From these two points, we can determine the slope of the line:
     \[
     \text{slope of } g(x) = \frac{0 - 2}{3 - 0} = -\frac{2}{3}
     \]
     Therefore, the equation of \( g(x) \) is:
     \[
     g(x) = -\frac{2}{3}x + 2
     \]

   - The graph \( f(x) \) passes through points (0, 6) and (9, 0). Similarly, the slope of \( f(x) \) is:
     \[
     \text{slope of } f(x) = \frac{0 - 6}{9 - 0} = -\frac{2}{3}
     \]
     Hence, the equation of \( f(x) \) is:
     \[
     f(x) = -\frac{2}{3}x + 6
     \]

2. **Translation vector**:
   Since the lines have the same slope, \( f(x) \) is a translated version of \( g(x) \). Comparing their y-intercepts, the translation in the vertical direction \( b \) is:
   \[
   b = 6 - 2 = 4
   \]
   The horizontal translation \( a \) can be determined by considering how far \( f(x) \) has shifted along the x-axis. The point \( (3, 0) \) on \( g(x) \) has been translated to \( (9, 0) \) on \( f(x) \), so:
   \[
   a = 9 - 3 = 6
   \]

3. **Sum of \( a \) and \( b \)**:
   \[
   a + b = 6 + 4 = 10
   \]

Therefore, there seems to be a mistake in the problem's answer choices, as the sum \( a + b = 10 \) is not listed.

Perhatikan grafik berikut. Jika f(x) merupakan grafik hasil translasi dari grafik g(x) oleh translasi T = (a, b), nilai dari a + b = ....

Learn how to solve a linear function translation problem with graphs f(x) and g(x). This problem explores the translation vector T = (a, b), using key mathematical concepts such as the slope formula and graph transformations. Suitable for students in Grades 9-11.

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