Answer:
5x -4y = 4
Explanation:
An equation for the perpendicular line can be found by swapping the x- and y-coefficients, and negating one of them. The constant changes to a value so that the equation is satisfied at the given point.
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Swapping the coefficients gives us ...
5x +4y = c . . . . . for some constant c
Negating the y-coefficient (so the x-coefficient remains positive) gives ...
5x -4y = c
constant
Putting (x, y) = (-4, -6) into the equation gives us the value of c:
5(-4) -4(-6) = c
-20 +24 = c = 4
equation
The line perpendicular to the given line and through the point (-4, -6) will have equation ...
5x -4y = 4