Find D Value 2147Bd

1. **State the problem:** We need to find the value of $d$ such that the point $(d, 4)$ lies on the line passing through $(0,7)$ and $(8,0)$. 2. **Find the equation of the line:** The slope $m$ of the line is given by $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 7}{8 - 0} = \frac{-7}{8}.$$ 3. Using point-slope form with point $(0,7)$: $$y - 7 = m(x - 0) \implies y - 7 = -\frac{7}{8}x.$$ 4. Simplify to slope-intercept form: $$y = 7 - \frac{7}{8}x.$$ 5. Substitute $y = 4$ to find $d$: $$4 = 7 - \frac{7}{8}d.$$ 6. Rearrange to isolate $d$: $$4 - 7 = -\frac{7}{8}d \implies -3 = -\frac{7}{8}d.$$ 7. Multiply both sides by $-\frac{8}{7}$ to solve for $d$: $$d = -3 \times \left(-\frac{8}{7}\right) = \frac{24}{7}.$$ 8. **Answer:** The value of $d$ is $$\boxed{\frac{24}{7}}.$$