Question

Use a table of values to determine what function produced the graph below?A- f(x)=1/2x-4B- f(x)=-1/2x+4C- f(x)=-2x-4D- f(x)=2x+4

Answer 1

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

`\begin{gathered} (x_1,y_1)\Rightarrow(8,0) \\ (x_2,y_2)\Rightarrow(0,-4) \end{gathered}`

To figure out the equation of the line, we will use the formula below

`\begin{gathered} (y_2-y_1)/(x_2-x_1)=(y-y_1)/(x-x_1) \\ \end{gathered}`

By substituting the values, we will have

`\begin{gathered} (y_(2)-y_(1))/(x_(2)-x_(1))=(y-y_(1))/(x-x_(1)) \\ (-4-0)/(0-8)=(y-0)/(x-8) \\ (-4)/(-8)=(y)/(x-8) \\ (1)/(2)=(y)/(x-8) \\ cross\text{ multiply, we will have} \\ 2y=1(x-8) \\ 2y=x-8 \\ divdie\text{ all through by 2} \\ (2y)/(2)=(x)/(2)-(8)/(2) \\ y=(1)/(2)x-4 \end{gathered}`

Graphically, we will have

Hence,

The final answer is

`\Rightarrow f(x)=(1)/(2)x-4`

OPTION A is the right answer