Write the equation of the line in standard form with integer

Write the equation of the line in standard form with integers only this perpendicular to the line 5x + 4y= 20 and containing the point (6,-8).

line perpendicular to 5x + 4y= 20 and containing the point (6,-8).

5x +4y = 20 ---> y = (-5/4)x +5 ---> slope = -5/4

slope of line perependicular to the above line : m = 1/(-5/4) = 4/5

Slope intercept form of equation : y = mx +c

y = 4x/5 +c .Find c using point ( 6, -8)

-8 = 4*6/5 +c-----> c = -8 -24/5 = -64/5

y = 4x/5 -64/5

5y = 4x -64