Question

home > leaked exams > june 2025 international form a (complete exam)
the table shows three values of x and their corresponding values of g(x), where $g(x)=\frac{f(x)}{x + 4}$? and f is a linear function. what is the y - intercept of the graph of y = f(x) in the xy - plane?
a (0, 36)
b (0, 9)
c (0, 4)
d (0, -9)

Explanation:

Step1: Use the given points to find $f(x)$ values

Since $g(x)=\frac{f(x)}{x + 4}$, when $x=-24$, $g(-24) = 3$. Then $3=\frac{f(-24)}{-24 + 4}$, so $f(-24)=3\times(-20)=-60$. When $x=-9$, $g(-9)=0$, then $0=\frac{f(-9)}{-9 + 4}$, so $f(-9)=0$. When $x = 16$, $g(16)=5$, then $5=\frac{f(16)}{16 + 4}$, so $f(16)=5\times20 = 100$.

Step2: Assume the linear - function form

Let $f(x)=mx + b$. We have the system of equations:

$$\begin{cases}-60=-24m + b\\0=-9m + b\\100=16m + b\end{cases}$$

. Subtract the second equation from the first equation: $-60-0=(-24m + b)-(-9m + b)$, which simplifies to $-60=-15m$, so $m = 4$.

Step3: Find the value of $b$

Substitute $m = 4$ into the equation $0=-9m + b$. We get $0=-9\times4 + b$, so $b = 36$.

Answer:

A. $(0,36)$