Question: Write this equation in slope intercept form: $y+6=-3(x+2)$
1. **State the problem:** We need to write the equation $y+6=-3(x+2)$ in slope-intercept form, which is $y=mx+b$ where $m$ is the slope and $b$ is the y-intercept.
2. **Start with the given equation:**
$$y+6=-3(x+2)$$
3. **Distribute the $-3$ on the right side:**
$$y+6=-3 \times x -3 \times 2$$
$$y+6=-3x -6$$
4. **Isolate $y$ by subtracting $6$ from both sides:**
$$y+6-6=-3x -6-6$$
$$y= -3x - \cancel{6} - \cancel{6}$$
5. **Simplify the constants:**
$$y=-3x -12$$
6. **Final slope-intercept form:**
$$y=-3x -12$$
This means the slope $m$ is $-3$ and the y-intercept $b$ is $-12$.