1. The problem asks for the equation of a line passing through the point $(-8,4)$ with slope $-\frac{7}{4}$. We want the equation in the form $y = -\frac{7}{4}x + b$ where $b$ is the y-intercept. 2. The formula for a line with slope $m$ passing through point $(x_1,y_1)$ is: $$y - y_1 = m(x - x_1)$$ 3. Substitute $m = -\frac{7}{4}$, $x_1 = -8$, and $y_1 = 4$: $$y - 4 = -\frac{7}{4}(x - (-8)) = -\frac{7}{4}(x + 8)$$ 4. Distribute the slope: $$y - 4 = -\frac{7}{4}x - \frac{7}{4} \times 8 = -\frac{7}{4}x - 14$$ 5. Add 4 to both sides to solve for $y$: $$y = -\frac{7}{4}x - 14 + 4 = -\frac{7}{4}x - 10$$ 6. Therefore, the missing value in the equation $y = -\frac{7}{4}x + \_$ is $-10$. Final answer: $$y = -\frac{7}{4}x - 10$$