Answer: The answer is (D) [tex]y-1=\dfrac{3}{2}(x+3).[/tex]
Step-by-step explanation: We are given to find the equation of a line which is parallel to the line in the graph and passing through the point (-3, 1).
The points (-2, -4) and (2, 2) lie on the line in the graph, so its slope will be
[tex]m=\dfrac{2+4}{2+2}=\dfrac{6}{4}=\dfrac{3}{2}.[/tex]
The slope of the line parallel to the line in the graph will also be same. Since the new line passes through the point (-3, 1), so the equation of the line will be
[tex]y=1=m(x+3)\\\\\Rightarrow y-1=\dfrac{3}{2}(x+3),[/tex]
which is in the slope-intercept form.
Thus, the correct option is (D).
