Question

What type of lines are  4x + 8y = 10 and  4x - 2y = 21 ?

Answer 1

`k:\ \ \ 4x + 8y = 10\ \ \ \Rightarrow\ \ \ 8y=-4x+10\ \ \ \Rightarrow\ \ \ y=- (1)/(2)x+1 (1)/(4)\\\\ \Rightarrow\ \ \ m_ 1=- (1)/(2) \\\\l:\ \ \ 4x - 2y = 21\ \ \ \Rightarrow\ \ \ -2y=-4x+21\ \ \ \Rightarrow\ \ \ y=2x-10 (1)/(2) \\\\\Rightarrow\ \ \ m_2=2\\\\m_1\cdot m_2=(- (1)/(2) )\cdot2=-1\ \ \ \Rightarrow\ \ \ k\ \perp\ l\\\\Ans.\ The\ lines\ are\ perpendicular.`

Answer 2

`4x + 8y = 10\\ 4x - 2y = 21 \\ \\ 8y =-4x+10 \ \ /:8 \\ -2y=-4x+21\ \ / : (-2)\\ \\y =-(4)/(8)x+(10)/(8)\\y=2x-(21)/(2)`


`y =-(1)/(2)x+(5)/(4)\\y=2x-10.5\\\\ a_(1)\cdot a_(2)=-1\\m_(1)=-(1)/(2), \ \ m_(2)=2 \\ m _(1)*m _(2) = -1 \ it \ perpendicular \ lines \ we \ have \\\\ m _(1)*m _(2) = -1\\\\-(1)/(2)\cdot 2 = -1\\-1=-1 \\ \\L=R`