Answer
$y = \frac{5}{2}x+27$
Work Step by Step
Given \begin{equation}
2 x+5 y=11\quad (-8,7)
\end{equation}
This is a linear function. Write the function as $y$ a function of $x$. \begin{equation}
\begin{aligned}
2 x+5 y&=11 \\
y&=\frac{11-2x}{5}\\
y &= -\frac{2}{5}x+\frac{11}{5}.
\end{aligned}
\end{equation} The line perpendicular to this line must have a slope given by:
$$ m_p = -\frac{1}{m} = -\frac{1}{-\frac{2}{5}}= \frac{5}{2}$$ The line may be written as $$y_p=\frac{5}{2}x+b.$$ Use the given point to find the $y$-intercept of the perpendicular line. \begin{equation}
\begin{aligned}
7&= 2.5\cdot (-8)+b \\
7&=-20+b\\
27&= b.
\end{aligned}
\end{equation} The equation of the perpendicular line is given by $$y = \frac{5}{2}x+27.$$
