#### Answer

$y-2=-\dfrac{1}{2}(x-1)$

#### Work Step by Step

The equation of a line in the point-slope form is the following:
$y-y_1=m(x-x_1)$, where $m$ is the slope and the point $(x_1,y_1)$ is on the graph.
In order to determine the equation of a line, we have to calculate the slope.
For this, we can use the rule, that the product of the slopes of two perpendicular lines equals $-1$.
Here, a perpendicular line is $y=2x$.
In this form, the slope can be seen as the coefficient of $x$, which is $2$
Therefore our line's slope $m$ can be calculated as:
$m\times2=-1$
$m=-\dfrac{1}{2}$
Therefore, using the point $(1, 2)$ and the slope $-\frac{1}{2}$, the equation can be written as:
$y-2=-\dfrac{1}{2}(x-1)$