Write an equation in standard form of the line that contains the point (-5,6) amd is perpendicular to 4x-y=3

4x - y = 3
y = 4x - 3
Slope = 4
Perpendicular slope = -1/4

y = mx + c
y = -1/4x+ c
at point (-5, 6),
6 = -1/4(-5) + c
6 = 5/4 + c
c = 6  - 5/4
c = 19/4

y = -1/4x + 19/4
4y = -x + 19

4x-y=3
-y=-4x+3
y=4x-3

Since it is perpendicular, the slope must be a negative reciprocal.

therefore the slope is -x/4

Substituting the x and the y values (to find the b)

6=5/4+b
6-5/4=b
19/4=b

therefore the equation of the line is
y=-x/4+19/4