1. **Stating the problem:** Given the table of points $(x,y)$: $$\begin{array}{cc} 4 & 0 \\ 8 & -5 \\ 12 & -10 \\ 16 & -15 \end{array}$$ We want to find the equation of the line that fits these points. 2. **Formula used:** The equation of a line is given by: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** The slope formula is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using points $(4,0)$ and $(8,-5)$: $$m = \frac{-5 - 0}{8 - 4} = \frac{-5}{4}$$ 4. **Check slope consistency:** Using points $(8,-5)$ and $(12,-10)$: $$m = \frac{-10 - (-5)}{12 - 8} = \frac{-5}{4}$$ Slope is consistent. 5. **Find y-intercept $b$:** Using point $(4,0)$ and slope $m = -\frac{5}{4}$: $$0 = -\frac{5}{4} \times 4 + b$$ $$0 = -5 + b$$ $$b = 5$$ 6. **Final equation:** $$y = -\frac{5}{4}x + 5$$ 7. **Explanation:** The line has a negative slope, meaning it goes down as $x$ increases, and crosses the y-axis at 5. **Answer:** $$y = -\frac{5}{4}x + 5$$