Question: line passing through $(-1,1)$ and $(-3,-5)$ what is the $y=$?
1. **State the problem:** Find the equation of the line passing through the points $(-1,1)$ and $(-3,-5)$.
2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$m=\frac{y_2 - y_1}{x_2 - x_1}.$$ The equation of the line in point-slope form is $$y - y_1 = m(x - x_1).$$
3. **Calculate the slope:**
$$m=\frac{-5 - 1}{-3 - (-1)}=\frac{-6}{-2}=3.$$
4. **Use point-slope form with point $(-1,1)$:**
$$y - 1 = 3(x - (-1))$$
$$y - 1 = 3(x + 1)$$
5. **Simplify:**
$$y - 1 = 3x + 3$$
$$y = 3x + 3 + 1$$
$$y = 3x + 4.$$
6. **Final answer:** The equation of the line is $$y = 3x + 4.$$