Question: What is the equation of the line that passes through the point $(-6,-4)$ and has a slope of $\frac{3}{1}$?
1. **State the problem:** Find the equation of the line passing through the point $(-6,-4)$ with slope $\frac{3}{1}$.
2. **Formula used:** The point-slope form of a line is given by
$$y - y_1 = m(x - x_1)$$
where $m$ is the slope and $(x_1,y_1)$ is a point on the line.
3. **Substitute known values:** Here, $m = \frac{3}{1} = 3$, $x_1 = -6$, and $y_1 = -4$. So,
$$y - (-4) = 3(x - (-6))$$
which simplifies to
$$y + 4 = 3(x + 6)$$
4. **Expand the right side:**
$$y + 4 = 3x + 18$$
5. **Isolate $y$ to get slope-intercept form:**
$$y = 3x + 18 - 4$$
$$y = 3x + 14$$
6. **Final answer:** The equation of the line is
$$y = 3x + 14$$