Question

Given a straight line ${30}^{\circ }+ysin{30}^{\circ }=2$ Determine the equation of the other line which is parallel to it and passes through (4, 3).

Answer 1

${30}^{\circ }+ysin{30}^{\circ }=2\Rightarrow x\frac{\sqrt{3}}{2}+y\frac{1}{2}=2\Rightarrow \sqrt{3}x+y=4y=-\sqrt{3}x+4\text{Slope of this line}=-\sqrt{3}\text{Slope of a line which is parallel to this given line}=-\sqrt{3}Let(4,3)=(x_1,y_1)\text{Thus, the equation of the required line is given by:}y-y_1=m_1(x-x_1)y-3=-\sqrt{3}(x-4)\sqrt{3}x+y=4\sqrt{3}+3$