Question: Convert to slope-intercept form.
y - 6 = 3(x + 2)
1. **State the problem:** Convert the equation $$y - 6 = 3(x + 2)$$ to slope-intercept form, which is $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept.
2. **Use the distributive property:** Expand the right side:
$$y - 6 = 3x + 6$$
3. **Isolate $$y$$:** Add 6 to both sides to solve for $$y$$:
$$y - 6 + 6 = 3x + 6 + 6$$
$$y = 3x + 12$$
4. **Final slope-intercept form:** The equation is now in the form $$y = mx + b$$ with slope $$m = 3$$ and y-intercept $$b = 12$$.
**Answer:** $$y = 3x + 12$$