Question: Find an equation of the line that passes through the point and has the indicated slope m. (Let x be the independent variable and y be the dependent variable.) (5, 8); m = - \frac{5}{2}
1. **State the problem:** Find the equation of the line passing through the point $(5, 8)$ with slope $m = -\frac{5}{2}$.
2. **Formula:** 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 values:** Using $(x_1, y_1) = (5, 8)$ and $m = -\frac{5}{2}$, we get
$$y - 8 = -\frac{5}{2}(x - 5)$$
4. **Simplify:** Distribute the slope on the right side
$$y - 8 = -\frac{5}{2}x + \frac{25}{2}$$
5. **Isolate $y$:** Add $8$ to both sides
$$y = -\frac{5}{2}x + \frac{25}{2} + 8$$
6. **Convert 8 to fraction:**
$$8 = \frac{16}{2}$$
7. **Add fractions:**
$$y = -\frac{5}{2}x + \frac{25}{2} + \frac{16}{2} = -\frac{5}{2}x + \frac{41}{2}$$
**Final answer:**
$$y = -\frac{5}{2}x + \frac{41}{2}$$