First, find the slope of the line defined by 5x3y8=0
5x  3y  8 = 0 add 8 to both sides
5x  3y = 8 subtract 5x from both sides
3y = 5x + 8 divide both sides by 3
y = (5/3)x  8/3 given that y = mx + b, where m is the slope, m = 5/3
a line perpendicular to this line has the negative inverse slope or, in this case, 3/5
use point slope to define your new line, (y  y1) = m(x  x1) with (x1,y1) = (6,6)
(y  6) = (3/5)(x  6) distribute the 3/5
y  6 = (3/5)x + 18/5 add 6 to both sides
y = (3/5)x + 48/5 ANSWER
5x  3y  8 = 0 add 8 to both sides
5x  3y = 8 subtract 5x from both sides
3y = 5x + 8 divide both sides by 3
y = (5/3)x  8/3 given that y = mx + b, where m is the slope, m = 5/3
a line perpendicular to this line has the negative inverse slope or, in this case, 3/5
use point slope to define your new line, (y  y1) = m(x  x1) with (x1,y1) = (6,6)
(y  6) = (3/5)(x  6) distribute the 3/5
y  6 = (3/5)x + 18/5 add 6 to both sides
y = (3/5)x + 48/5 ANSWER

you are welcome, Fiona was on the right track but she had to get the equation into slopeintercept form before determining the slope!!!!
Report Abuse

The slope of that line is 5, and the slope of a perpendicular line is its negative reciprocal. So the equation would be y6= 1/5 (x6) in point slope from. In slope intercept it would be y=1/5x +4.8, with 4.8 being the y intercept, and 1/5 being the slope. Hope I'm right.