Question: Write the following inequality in slope-intercept form.
$$16x + 7y \leq -16$$
Write your answer with $y$ first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.
y \leq
1. **State the problem:** We need to rewrite the inequality $$16x + 7y \leq -16$$ in slope-intercept form, which means solving for $y$ so that the inequality looks like $$y \leq mx + b$$ where $m$ and $b$ are constants.
2. **Isolate $y$:** Start by subtracting $16x$ from both sides:
$$16x + 7y \leq -16$$
$$7y \leq -16 - 16x$$
3. **Divide both sides by 7:** Since 7 is positive, the inequality direction stays the same.
$$y \leq \frac{-16 - 16x}{7}$$
4. **Separate the fraction:**
$$y \leq \frac{-16}{7} - \frac{16x}{7}$$
5. **Rewrite in slope-intercept form:**
$$y \leq -\frac{16}{7}x - \frac{16}{7}$$
**Final answer:**
$$y \leq -\frac{16}{7}x - \frac{16}{7}$$
This is the inequality in slope-intercept form with $y$ isolated and the inequality symbol preserved.