1. **State the problem:** Find the equation of the straight line passing through the points $(-2,8)$, $(0,0)$, and $(2,-8)$. 2. **Formula used:** The equation of a line can be found using the slope-intercept form: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** The slope between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using points $(-2,8)$ and $(0,0)$: $$m = \frac{0 - 8}{0 - (-2)} = \frac{-8}{2} = -4$$ 4. **Find the y-intercept $b$:** Since the line passes through $(0,0)$, the y-intercept is $$b = 0$$ 5. **Write the equation:** Substitute $m = -4$ and $b = 0$ into the slope-intercept form: $$y = -4x + 0$$ or simply $$y = -4x$$ 6. **Verify with the third point $(2,-8)$:** Substitute $x=2$: $$y = -4(2) = -8$$ which matches the given point, confirming the equation is correct.