To determine which of the options best defines the table, we will have to determine the equation of the line that defines the table.
To find the equation of a line
let us select the first two points of the table
[tex]\begin{gathered} \text{when } \\ x=-4,\text{ y=2} \\ \text{when} \\ x=-2,\text{ y=1} \end{gathered}[/tex]
We can now use the equation of the line formula
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ \\ \frac{y-2}{x-(-4)}=\frac{1-2}{-2-(-4)} \\ \\ \frac{y-2}{x+4}=\frac{1-2}{-2+4} \\ \\ \frac{y-2}{x+4}=\frac{-1}{2} \end{gathered}[/tex]
The next step will be
to cross multiply
[tex]y-2=-\frac{1}{2}(x+4)[/tex]
To find the option that conforms to the expression
[tex]\begin{gathered} \text{let us add 5 to both sides} \\ y-2+5=-\frac{1}{2}(x+4)+5 \\ \\ y+3=-\frac{1}{2}x-2+5 \\ y+3=-\frac{1}{2}x+3 \\ \text{This is equivalent to} \\ y+3=-\frac{1}{2}(x-6) \end{gathered}[/tex]
ThusThe correct answer is option C
