To solve for the missing coordinate $y$ in point $A(8, y)$, given the slope between points $A(8, y)$ and $B(24, 5)$ is $\frac{9}{4}$, we use the slope formula:

$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}.$

Substituting the given values: $\frac{9}{4} = \frac{5 - y}{24 - 8}.$

Simplify the denominator: $\frac{9}{4} = \frac{5 - y}{16}.$

Cross-multiply to eliminate the fractions: $9 \cdot 16 = 4 \cdot (5 - y).$

Simplify both sides: $144 = 20 - 4y.$

Rearrange to isolate $y$: $144 - 20 = -4y.$

$124 = -4y.$

Solve for $y$: $y = \frac{-124}{-4} = 31.$

Thus, the missing coordinate is: $y = 31.$

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Related Questions:

1. How do you verify if the calculated slope matches the given value?
2. What happens if a different slope is provided between these points?
3. Can the slope formula be used for vertical or horizontal lines? Why or why not?
4. How does changing either coordinate affect the slope?
5. How would this process differ if both $x$-coordinates were missing?

Tip: Always check the direction of the slope (positive or negative) to confirm your solution aligns with the given problem.