Answer
$\color{blue}{y=-\dfrac{1}{2}x+\dfrac{5}{2}}$.
Work Step by Step
RECALL:
(1) The slope-intercept form of a line's equation is:
$y=mx+b$
where $m$=slope and $b$ = y-intercept.
(2) Perpendicular lines have inverse reciprocal slopes.
Line $L$ is perpendicular to the line $y=2x$, whose slope is $2$.
Since $L$ is perpendicular to this line, $L$ has a slope of $-\dfrac{1}{2}$.
Thus, the tentative equation of the line is $y=-\dfrac{1}{2}x+b$.
To find the value of $b$, substitute the x and y values of the point $(1, 2)$ into the tentative equation above to obtain:
$y=-\dfrac{1}{2}x+b
\\2=-\dfrac{1}{2}(1) + b
\\2=-\dfrac{1}{2}+ b
\\2+\dfrac{1}{2}=b
\\\dfrac{4}{2}+\dfrac{1}{2}=b
\\\dfrac{5}{2}=b$
Therefore, the equation of line $L$ is $\color{blue}{y=-\dfrac{1}{2}x+\dfrac{5}{2}}$.
