Answer:
x +2y = -2
Explanation:
You want the line perpendicular to 2x-y = 5 that passes through (6, -4).
Perpendicular line
The slopes of perpendicular lines are opposite reciprocals. This means the equation of the perpendicular line can be formed by swapping the coefficients of x and y, and negating one of them. We want the leading coefficient to be positive, so we choose our line's equation to be ...
2x -y = constant . . . . . . . . . . original line
x +2y = <some constant>
The constant must be chosen so the equation is true at the given point:
x + 2y = (6) +2(-4) = -2
An equation for the perpendicular line is ...
x +2y = -2