## Intermediate Algebra: Connecting Concepts through Application

$\color{blue}{y=-\dfrac{1}{2}x+7.5}$
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 $\color{blue}{y=-\dfrac{1}{2}x+7.5}$.