When 2 straight lines, line 1 of slope m and line 2 of slope n, intersect perpendicularly to each other, use the fact that the product of those 2 slopes is always negative 1: m×n=‐1 (m,n≠0). In other words, m and n are the reciprocal of the other's: m=‐1/n, or n=‐1/m.

Let the given equation of slope m be line 1, and simplify it. Line 1: 4y=‐x+7 ⇒ y=‐(1/4)x+7/4 ⇒ the slope m=‐1/4 ⇒ the slope of the other line: n=‐1/m=‐1/(‐1/4)=4

Let the line of slope n that passes thru a point (a,b) be line 2. Line 2 is written as follows: y‐b=n(x‐a). Plug n=4, a=‐5 and b=6 into the equation shown above and simplify it. y‐6=4(x+5)⇒ y=4x+26

Therefore the equation of the line that passes thru (‐5,6) and is perpendicular to the line 4y=‐x+7 is y=4x+26.