Answer:
[tex]y = - 6x - 2[/tex]
Explanation
The given line is
[tex]6x - 36y = k[/tex]
where k is the missing constant from the given equation( this has no effect on the solution in anyway)
We solve for y to get;
[tex]y = \frac{1}{6}x - \frac{k}{36} [/tex]
The slope of this line after comparing to
y=mx+c is
[tex]m = \frac{1}{6} [/tex]
The negative reciprocal is m=-6
The equation of the required line that passes through (-5,4) is given by
[tex]y - 4 = - 6(x - - 5)[/tex]
We multiply through by 6 to get:
[tex]y - 4 = - 6x - 30[/tex]
We expand to get;
[tex]y = - 6x - 26[/tex]
