https://file.aiquickdraw.com/mathbot/file/1725988805345o07xw5vl.jpg

The given function is:

\[
f(x) = \frac{2}{3}(x + 5)
\]

You are asked to find \( f(6.7) \).

### Step-by-step solution:

1. Substitute \( x = 6.7 \) into the function:
   \[
   f(6.7) = \frac{2}{3}(6.7 + 5)
   \]

2. Simplify the expression inside the parentheses:
   \[
   6.7 + 5 = 11.7
   \]
   So,
   \[
   f(6.7) = \frac{2}{3} \times 11.7
   \]

3. Multiply \( \frac{2}{3} \) by \( 11.7 \):
   \[
   f(6.7) = \frac{2 \times 11.7}{3} = \frac{23.4}{3} = 7.8
   \]

Thus, the value of \( f(6.7) \) is:

\[
f(6.7) = 7.8
\]

Do you want more details or have any questions?

Here are some related questions to explore:
1. What is the general process to evaluate a function at a given point?
2. How does the distributive property help simplify expressions like \( \frac{2}{3}(x + 5) \)?
3. What would the graph of \( f(x) = \frac{2}{3}(x + 5) \) look like?
4. How does changing the coefficient \( \frac{2}{3} \) affect the slope of the line?
5. Can we generalize the behavior of linear functions when evaluated at different values?

**Tip:** When working with fractional coefficients, it's often easier to deal with them by multiplying the numerator and denominator separately before dividing.

Learn how to evaluate the linear function f(x) = (2/3)(x + 5) by substituting x = 6.7. This problem demonstrates key algebraic concepts suitable for students in Grades 8-10.

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