Finite Mathematics, Chapter 1, Review Exercises, Section Review Exercises, Problem 20

Determine an equation in the form $y = mx + b$ (where possible) for the line
that goes through $(0, 5)$ and is perpendicular to $8x + 5y = 3$
If we transform the given line into point slope form, we have

$
\begin{equation}
\begin{aligned}
8x + 5y &= 3 \\
\\
5y &= -8x + 3\\
\\
y &= \frac{-8}{5}x + \frac{3}{5}
\end{aligned}
\end{equation}
$


Now that the line is in the slope intercept form $y = mx + b$. By observation, $\displaystyle m = \frac{-8}{5}$. Thus,
the slope of perpendicular line is
$\displaystyle m_{\perp} = -\frac{1}{\left( \frac{-8}{5} \right)} = \frac{5}{8}$

Also, we know that the given point is the $y$-intercept $b = 5$. Therefore, by using the slope intercept form, the equation
of the line will be $\displaystyle y = mx + b = \frac{5}{8}x + 5 $