Answer:
[tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
We have the slope value of the first line, we will call this [tex]m_{1}[/tex]
so [tex]m_{1}=2[/tex]
And we use the condition so that two lines are perpendicular: the product of the two slopes must be equal to -1.
That is, if the slope of the first line is [tex]m_{1}[/tex] and the slope of the second line is [tex]m_{2}[/tex]:
[tex]m_{1*}m_{2}=-1[/tex]
we know that [tex]m_{1}=2[/tex], so:
[tex]2m_{2}=-1[/tex]
and clearing for [tex]m_{2}[/tex]:
[tex]m_{2}=-\frac{1}{2}[/tex]
the slope of the line perpendicular to the line with a slope of 2 is: [tex]-\frac{1}{2}[/tex]
