Question: Find an equation of the line having the given characteristics: $x$-intercept=$2$; containing the point $(4,-5)$
1. **State the problem:** Find the equation of a line with $x$-intercept $2$ and passing through the point $(4,-5)$.
2. **Recall the formula:** The $x$-intercept means the line crosses the $x$-axis at $(2,0)$.
3. **Use the two points:** We have points $(2,0)$ and $(4,-5)$.
4. **Calculate the slope $m$:**
$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - 0}{4 - 2} = \frac{-5}{2}$$
5. **Use point-slope form:**
$$y - y_1 = m(x - x_1)$$
Using point $(2,0)$:
$$y - 0 = -\frac{5}{2}(x - 2)$$
6. **Simplify:**
$$y = -\frac{5}{2}x + 5$$
7. **Final answer:** The equation of the line is
$$y = -\frac{5}{2}x + 5$$