Answer:
y = -8/5x + 2/5
Explanation:
First let's find the y-intercept of 3x+5y=2 by solving for y (putting into slope-intercept form)
5y = -3x + 2
y= -3/5x + 2/5
The y-intercept is 2/5
A perpendicular line has the opposite reciprocal slope. We need to find the slope of 5x-8y=3 by solving for y as well.
-8y = -5x + 3
y = 5/8x - 3/8
The slope is 5/8
The opposite reciprocal would be -8/5
Putting the y-int and slope together in slope-intercept form for the new line... y = -8/5x + 2/5