Answer: The correct option is
(A) [tex]y+5=2(x+2).[/tex]
Step-by-step explanation: We are given to use the co-ordinates of the labelled point to find a point-slope equation of the graphed line.
We note from the graph that
the co-ordinates of the labelled point are (-2, -5) and one of the other points that lies on the line is (0, -1).
Since the labelled point also lie on the line, so the slope of the graphed line will be
[tex]m=\dfrac{-1-(-5)}{0-(-2)}=\dfrac{-1+5}{0+2}=\dfrac{4}{2}=2.[/tex]
Since the line passes through the point (-2, -5), so the point slope fom of the equation of the line is given by
[tex]y-(-5)=m(x-(-2))\\\\\Rightarrow y+5=2(x+2).[/tex]
Thus, the required point-slope form of the equation of the line is [tex]y+5=2(x+2).[/tex]
Option (A) is CORRECT.
