Answer: The correct option is
(A) [tex]y=-\dfrac{3}{2}x-\dfrac{9}{2}.[/tex]
Step-by-step explanation: We are given to find the equation of the graphed straight line in slope-intercept form.
From the graph, we note that
the straight line passes through the points (-3, 0) and (-1, -3).
The SLOPE of a straight line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
So, the slope of the graphed line will be
[tex]m=\dfrac{-3-0}{-1-(-3)}=\dfrac{-3}{-1+3}=-\dfrac{3}{2}.[/tex]
Since the line passes through the point (-3, 0), so its equation is given by
[tex]y-0=m(x-(-3))\\\\\\\Rightarrow y=-\dfrac{3}{2}(x+3)\\\\\\\Rightarrow y=-\dfrac{3}{2}x-\dfrac{9}{2}.[/tex]
Thus, the required equation of the graphed line in slope-intercept form is [tex]y=-\dfrac{3}{2}x-\dfrac{9}{2}.[/tex]
Option (A) is CORRECT.
