Question

Which bests represents the line defined by the table of ordered pairs

Answer 1

We are given the different values for x and y in the table to be

`\begin{gathered} (2,0) \\ (2,-2) \\ (2,3) \end{gathered}`

To get the option that best defines the table

We can get the equation of a line that conforms to the given points

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)`

So we can use the first two points

`(2,0)\text{ and (2,-2)}`

`\begin{gathered} (y-0)/(x-2)=(-2-0)/(2-2) \\ \\ (y)/(x-2)=-(2)/(0) \end{gathered}`

If we cross multiply

`\begin{gathered} y*0=2(x-2) \\ 0=2x-4 \\ 2x=4 \\ x=(4)/(2) \\ x=2 \end{gathered}`

Thus the equation of the line is

`x=2`

The graph of the function is given as

`x=2`

The graph of the function is

The best option that best defines the function is option D