Answer
$\color{blue}{y=-\dfrac{1}{2}x+7.5}$
Work Step by Step
Recall:
The slope of two perpendicular lines are negative reciprocals (product is $-1$) of each other.
Since the line is perpendicular to $y=2x-1$ (whose slope is $2$), then the slope of the line must be $\dfrac{-1}{2}$.
Thus, the tentative equation of the line is $y=-\dfrac{1}{2}x+b$.
The line passes through $(1, 7)$ so to find the value of $b$, susbtitute the $x$ and $y$ values of this point into the tentative equation above to obtain:
\begin{align*}
y&=-\frac{1}{2}x+b\\\\
7&=-\frac{1}{2}(1)+b\\\\
7&=-\frac{1}{2}+b\\\\
7+\frac{1}{2}&=b\\\\
7.5&=b
\end{align*}
Therefore, the equation of the line is $\color{blue}{y=-\dfrac{1}{2}x+7.5}$.
