Since the given line
[tex]y = \frac{ 1}{4} x - 3[/tex]
has slope
[tex] = \frac{1}{4} [/tex]
The equation of the line perpendicular to it must have a slope which is the negative reciprocal of ,
[tex] \frac{1}{4} [/tex]
The slope of the perpendicular line
[tex] = \frac{ - 1}{ \frac{1}{4} } = - 4[/tex]
Using the slope intercept form,
[tex]y = mx + c[/tex]
We substitute
[tex] - 4[/tex]
This implies that,
[tex]y = - 4x + c[/tex]
Since
[tex](-2,4) [/tex]
lies on this line , it must satisfy its equation.
That is
[tex]4 = - 4( - 2) + c[/tex]
This implies that
[tex]4 = 8 + c[/tex]
[tex]4 - 8 = c[/tex]
[tex]c = - 4[/tex]
The line therefore has equation,
[tex]y = - 4x - 4[/tex]
