Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? check all that apply.

5x - 2y = -6 
-2y = -5y - 6
y = 5/2y + 3slope here is 5/2. A perpendicular slope will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So we need a slope of -2/5.
now we use y = mx + b
slope(m) = -2/5
(5,-4)...x = 5 and y = -4
now we sub
-4 = -2/5(5) + b
-4 = -2 + b
-4 + 2 = b
-2 = b
perpendicular line is : y = -2/5x - 2 or 2x - 5y = -10