Two equal sides of an isosceles triangle are given by equation 7x-y+3=0 and x + y - 3 = 0. The slope of the third side is

Slopes of the given lines are 7 , - 1 . Let m be the slope of third side'
Third side makes equal angles with the given sides
$\begin{array}{l}\Rightarrow \left|\frac{\mathrm{m}-7}{1+7\mathrm{m}}\right|=\left|\frac{\mathrm{m}+1}{1-\mathrm{m}}\right|\Rightarrow \frac{\mathrm{m}-7}{1+7\mathrm{m}}=\pm \frac{\mathrm{m}+1}{1-\mathrm{m}}\Rightarrow (7\mathrm{m}+1)(\mathrm{m}+1)=\pm (\mathrm{m}-7)(1-\mathrm{m})\\ \Rightarrow 7{\mathrm{m}}^2+8\mathrm{m}+1=\pm \left(8\mathrm{m}-7-{\mathrm{m}}^2\right)\Rightarrow 8{\mathrm{m}}^2+8=0 \mathrm{or} 6{\mathrm{m}}^2+16\mathrm{m}-6=0\\ \Rightarrow 3{\mathrm{m}}^2+8\mathrm{m}-3=0\Rightarrow (\mathrm{m}+3)(3\mathrm{m}-1)=0\Rightarrow \mathrm{m}=-3 \mathrm{or} 1/3\end{array}$