Answer :
Given:
The line is perpendicular to the line whose equation is
[tex]y\text{ = }\frac{1}{4}x\text{ + 5}[/tex]It passes through the point (6, -5)
A line with a slope (m) is perpendicular with another line with a slope (m*) if:
[tex]m\text{ }\times m^{\cdot}\text{ = -1}[/tex]The slope of the line would thus be:
[tex]\begin{gathered} \text{slope = }\frac{-1}{\frac{1}{4}} \\ =\text{ -4} \end{gathered}[/tex]In point-slope form:
[tex]\begin{gathered} y\text{ - (-5) = -4(x-6)} \\ y\text{ + 5 = -4(x -6)} \end{gathered}[/tex]In slope-intercept form:
[tex]\begin{gathered} y+\text{ 5 = -4(x-6)} \\ y\text{ + 5 = -4x + 24} \\ y\text{ = -4x + 24 - 5} \\ y\text{ = -4x + 19} \end{gathered}[/tex]