For a line, a symmetric line is any perpendicular line to it, because if you drop a perpendicular line, the line on one side is just a reflection of the other side.
so, in short, what is a likely equation of a line perpendicular to that one?
well, what's the slope of the line on the graph anyway? well, notice, we have a point of (-3,-4), let's pick another point on the line to get its slope, hmmm say (0,8),
![\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{8}) \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{8-(-4)}{0-(-3)}\implies \cfrac{8+4}{0+3}\implies \cfrac{12}{3}\implies 4](https://tex.z-dn.net/?f=%5Cbf%20%28%5Cstackrel%7Bx_1%7D%7B-3%7D~%2C~%5Cstackrel%7By_1%7D%7B-4%7D%29%5Cqquad%20%0A%28%5Cstackrel%7Bx_2%7D%7B0%7D~%2C~%5Cstackrel%7By_2%7D%7B8%7D%29%0A%5C%5C%5C%5C%5C%5C%0A%25%20slope%20%20%3D%20m%0Aslope%20%3D%20%20m%5Cimplies%20%0A%5Ccfrac%7B%5Cstackrel%7Brise%7D%7B%20y_2-%20y_1%7D%7D%7B%5Cstackrel%7Brun%7D%7B%20x_2-%20x_1%7D%7D%5Cimplies%20%5Ccfrac%7B8-%28-4%29%7D%7B0-%28-3%29%7D%5Cimplies%20%5Ccfrac%7B8%2B4%7D%7B0%2B3%7D%5Cimplies%20%5Ccfrac%7B12%7D%7B3%7D%5Cimplies%204)
![\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{4\implies \cfrac{4}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{1}{4}}\qquad \stackrel{negative~reciprocal}{-\cfrac{1}{4}}}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Bperpendicular%20lines%20have%20%5Cunderline%7Bnegative%20reciprocal%7D%20slopes%7D%7D%0A%7B%5Cstackrel%7Bslope%7D%7B4%5Cimplies%20%5Ccfrac%7B4%7D%7B1%7D%7D%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cstackrel%7Breciprocal%7D%7B%5Ccfrac%7B1%7D%7B4%7D%7D%5Cqquad%20%5Cstackrel%7Bnegative~reciprocal%7D%7B-%5Ccfrac%7B1%7D%7B4%7D%7D%7D)
so, a line whose slope is -1/4 is a likely line of symmetry for that line, since it'd be a perpendicular line to it, and since you know your slope-intercept forms, you know which one that is.