Answer: The correct option is
(A) \(y+4=\dfrac{1}{2}(x+4).\)
Step-by-step explanation: We are given to find the equation of the graphed line in point-slope form.
POINT-SLOPE FORM: The point-slope form of a line with slope 'm' and passing through a point (a, b) is given by
\(y-b=m(x-a).\)
From the graph, we note that the points (4, 0) and (-4, -4) are two points on the straight line.
So, the slope of the line is
\(m=\dfrac{-4-0}{-4-4}\\\\\\\Rightarrow m=\dfrac{1}{2}.\)
Also, the line passes through the point (-4, -4), so the equation of the line is
\(y-(-4)=m(x-(-4))\\\\\Rightarrow y+4=\dfrac{1}{2}(x+4).\)
Thus, the required point-slope form of the graphed line is
\(y+4=\dfrac{1}{2}(x+4).\)
