Given an equation of the line of the following form:
[tex]y=mx+b[/tex]
we know that 'm' denotes the slope of the line, then, the slope of a perpendicular line can be found with the following equation:
[tex]m_p=-\frac{1}{m}[/tex]
in this case, we have the following:
[tex]\begin{gathered} m=-\frac{1}{5} \\ \Rightarrow m_p=-\frac{1}{-\frac{1}{5}}=5 \\ m_p=5 \end{gathered}[/tex]
therefore, an equation fo a line that is perpendicular to y = -1/5x+4 is:
[tex]y=5x+4[/tex]
