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Hi,
Using the standard slope-intercept form for an equation of a line y = mx + b
where m is the slope and b the y-intercept.
line whose x intercept is -3 and which is perpendicular to the line 3x+5y-8=0
3x + 5y - 8 = 0 OR 
New Line perpendicular to the above: m = 5/3
y = (5/3)x + b
0 = (5/3)·-3 + b |Using x-intercept = -3: |(x,y):(-3,0) to solve for b
5 = b
y = (5/3)x + 5