Question: Evaluate $2x + 6y$ when $x = -\frac{4}{5}$ and $y = \frac{1}{3}$. Write your answer as a fraction or mixed number in simplest form.
1. **State the problem:** We need to evaluate the expression $$2x + 6y$$ given $$x = -\frac{4}{5}$$ and $$y = \frac{1}{3}$$.
2. **Write the expression with substituted values:**
$$2\left(-\frac{4}{5}\right) + 6\left(\frac{1}{3}\right)$$
3. **Multiply the constants:**
$$= -\frac{8}{5} + \frac{6}{3}$$
4. **Simplify the second fraction:**
$$\frac{6}{3} = 2$$
So the expression becomes:
$$-\frac{8}{5} + 2$$
5. **Convert 2 to a fraction with denominator 5:**
$$2 = \frac{10}{5}$$
6. **Add the fractions:**
$$-\frac{8}{5} + \frac{10}{5} = \frac{-8 + 10}{5} = \frac{2}{5}$$
7. **Final answer:**
The value of the expression is $$\frac{2}{5}$$, which is already in simplest form.