Question

Does the given equation of line form parallel lines or not

Answer 1

`k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\k\ \perp\ l\iff m_1\cdot m_2=-1\\\\k\ ||\ l\iff m_1=m_2`

`k:x+4y=10\ \ \ |-x\\\\4y=-x+10\ \ \ \ |:4\\\\y=-(1)/(4)x+(10)/(4)\to m_1=-(1)/(4)\\\\l:3x-2y=5\ \ \ \ |-3x\\\\-2y=-3x+5\ \ \ \ |:(-2)\\\\y=(3)/(2)x-(5)/(2)\to m_2=(3)/(2)`

`m_1\\eq m_2\to\text{ no parallel}\\\\m_1\cdot m_2=-(1)/(4)\cdot(3)/(2)\\eq-1\to\text{ no perpendicular}`

Answer: NOT PARALLEL