.
#y=1/2x-1#
This is in the form of:
#y=mx+b# where #m# is the slope which in this case is #1/2#.
Let's call this slope #m_1=1/2#
For a line to be perpendicular to this, we need to have:
#m_1m_2=-1# where #m_2# is the slope of the perpendicular line.
#m_2=-1/m_1=-1/(1/2)=-1(2)=-2#
#y=-2x+b#
Because #b# can be any value, there are infinite solutions to this problem as there could be infinite different lines perpendicular to another line. To fine a specific one, we need to know the coordinates of the point where this line meets the original line. Then using those coordinates in its equation, we can solve for #b#.
