Question

What is perpendicular to 2x-y=1 and contains (4, -6)? Please show your work!

Answer 1

`k:\ y=m_1x+b_1\\\\l:\ y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\\\\\text{We have}\\\\k:\ 2x-y=1\ \ \ |-2x\\-y=-2x+1\ \ \ \ |\cdot(-1)\\y=2x-1\to m_1=2\\\\l:\ y=m_2x+b\\\\l\ \perp\ k\iff 2m_2=-1\ \ \ \ |:2\to m_2=-0.5\\\\l:\ y=-0.5x+b\\\\\text{The line l contains (4, -6)}\\\\\text{Put the values of coordinates to the equation of line l}\\\\-6=-0.5(4)+b\\-6=-2+b\ \ \ \ \ |+2\\b=-4\\\\Answer:\ y=-0.5x-4\to x+y=-8`