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.