Answer:
Concept:
To figure out the equation of the graph, we will use the image below and bring out the two intercepts
The two intercepts from the graph are
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(8,0) \\ (x_2,y_2)\Rightarrow(0,-4) \end{gathered}[/tex]
To figure out the equation of the line, we will use the formula below
[tex]\begin{gathered} \frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \\ \end{gathered}[/tex]
By substituting the values, we will have
[tex]\begin{gathered} \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{y-y_{1}}{x-x_{1}} \\ \frac{-4-0}{0-8}=\frac{y-0}{x-8} \\ \frac{-4}{-8}=\frac{y}{x-8} \\ \frac{1}{2}=\frac{y}{x-8} \\ cross\text{ multiply, we will have} \\ 2y=1(x-8) \\ 2y=x-8 \\ divdie\text{ all through by 2} \\ \frac{2y}{2}=\frac{x}{2}-\frac{8}{2} \\ y=\frac{1}{2}x-4 \end{gathered}[/tex]
Graphically, we will have
Hence,
The final answer is
[tex]\Rightarrow f(x)=\frac{1}{2}x-4[/tex]
OPTION A is the right answer
