Answer: 45

Explanation:1. Understand the problem: A table provides three pairs of $(x, g(x))$ values. We are given that $g(x) = \dfrac{f(x)}{x+5}$, and $f(x)$ is a linear function. We need to find the y-coordinate of the y-intercept of the graph of $y=f(x)$.

Table values: $x = -25, g(x) = 4$ $x = -9, g(x) = 0$ $x = 15, g(x) = 6$

2. Set up the linear function and relate it to $g(x)$: Let the linear function be $f(x) = mx + c$, where $c$ is the y-intercept we need to find. From $g(x) = \dfrac{f(x)}{x+5}$, we have $f(x) = g(x)(x+5)$.

3. Use the table values to form equations for $f(x)$: Using $x = -25, g(x) = 4$: $f(-25) = 4(-25+5) = 4(-20) = -80$. Since $f(x) = mx+c$, we have $-25m + c = -80$ (Equation 1).

Using $x = -9, g(x) = 0$: $f(-9) = 0(-9+5) = 0(-4) = 0$. So, $-9m + c = 0$ (Equation 2).

4. Solve the system of linear equations for $m$ and $c$: From Equation 2, $c = 9m$. Substitute $c = 9m$ into Equation 1: $-25m + 9m = -80$ $-16m = -80$ $m = \dfrac{-80}{-16} = 5$. Now find $c$ using $c = 9m$: $c = 9(5) = 45$.

5. Verify with the third point (optional): Using $x = 15, g(x) = 6$: $f(15) = 6(15+5) = 6(20) = 120$. Check if $f(15) = 5(15) + 45$: $75 + 45 = 120$. This matches, so our values for $m$ and $c$ are consistent.

6. Identify the y-intercept: The y-intercept of $f(x) = mx+c$ is $c$.

7. Conclusion: The y-coordinate of the y-intercept of the graph of $y=f(x)$ is 45.