Question: 4.
The slope is $-\frac{1}{3}$. The point $(6, 0)$ lies on the line.
1. **State the problem:** We need to find the equation of a line with slope $m = -\frac{1}{3}$ that passes through the point $(6, 0)$.
2. **Formula used:** The point-slope form of a line is given by:
$$y - y_1 = m(x - x_1)$$
where $(x_1, y_1)$ is a point on the line and $m$ is the slope.
3. **Substitute known values:** Here, $m = -\frac{1}{3}$, $x_1 = 6$, and $y_1 = 0$. So,
$$y - 0 = -\frac{1}{3}(x - 6)$$
4. **Simplify the equation:**
$$y = -\frac{1}{3}x + \frac{1}{3} \times 6$$
$$y = -\frac{1}{3}x + 2$$
5. **Final equation:** The equation of the line is
$$y = -\frac{1}{3}x + 2$$
This means the line has a slope of $-\frac{1}{3}$ and crosses the y-axis at $2$.