Question

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

Answer 1

$k:\ y=m_1x+b_1\\\\l:\ y=m_2x+b_2\\\\l\ ||\ k\iff m_1=m_2\\\\\text{We have}\\\\k:\ 2x-y=1\ \ \ |-2x\\-y=-2x+1\ \ \ \ |\cdot(-1)\\y=2x-1\to m_1=2\\\\l:\ y=m_2x+b\\\\l\ ||\ k\iff m_2=2\\\\l:\ y=2x+b\\\\\text{The line l contains (4, -6)}\\\\\text{Put the values of coordinates to the equation of line l}\\\\-6=2(4)+b\\-6=8+b\ \ \ \ \ |-8\\b=-14\\\\Answer:\ y=2x-14\to 2x-y=14$