Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
I will call [tex]m_{a}[/tex] the slope of line [tex]a[/tex], and [tex]m_{b}[/tex] the slope of line [tex]b[/tex].
For two lines to be perpendicular, the following must be satisfied:
[tex]m_{a}*m_{b}=-1[/tex]
in this case we know:
[tex]m_{a}=-2[/tex]
so:
[tex](-2)*m_{b}=-1[/tex]
And clearing for the slope of line [tex]b[/tex]:
[tex]m_{b}=\frac{-1}{-2} \\m_{b}=\frac{1}{2}[/tex]
The slope of the line [tex]b[/tex] which is perpendicular to line [tex]a[/tex] is [tex]\frac{1}{2}[/tex]
