Answer
$y=\dfrac{4}{5}(x-6)$
Work Step by Step
Using the properties of equality, the given linear equation, $
5x+4y=1
$ is equivalent to
\begin{array}{l}
4y=-5x+1
\\\\
y=-\dfrac{5}{4}x+\dfrac{1}{4}
.\end{array}
Using $y=mx+b$ or the Slope-Intercept form where $m$ is the slope, then the slope of the given line is $
-\dfrac{5}{4}
$. Since perpendicular lines have negative reciprocal slopes, then the needed linear equation has slope equal to $
\dfrac{4}{5}
$. Since it also passes through the given point $(
6,0
)$, then using $y-y_1=m(x-x_1)$ or the Point-Slope form where $m$ is the slope and $(x_1,y_1)$ is a point on the line, the equation of the needed line is
\begin{array}{l}
y-0=\dfrac{4}{5}(x-6)
\\\\
y=\dfrac{4}{5}(x-6)
.\end{array}
