Question: What is an equation of the line that passes through the points $(1,6)$ and $(4,3)$?
1. **State the problem:** Find the equation of the line passing through points $(1,6)$ and $(4,3)$.
2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by:
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
3. **Calculate the slope:**
$$m = \frac{3 - 6}{4 - 1} = \frac{-3}{3} = -1$$
4. **Use point-slope form:**
The equation of a line with slope $m$ passing through point $(x_1,y_1)$ is:
$$y - y_1 = m(x - x_1)$$
5. **Substitute values:**
Using point $(1,6)$ and slope $-1$:
$$y - 6 = -1(x - 1)$$
6. **Simplify:**
$$y - 6 = -x + 1$$
7. **Isolate $y$:**
$$y = -x + 1 + 6$$
$$y = -x + 7$$
**Final answer:** The equation of the line is $$y = -x + 7$$.