The slope-intercept form of an equation is useful for finding the slope, and for comparing lines (parallel or perpendicular).
The equation is y=mx+b where m is the slope. Two lines are perpendicular if their slopes are negative reciprocals of each other. That is, if the product of the slopes is -1.
2x - 5y = -3
Subtract x from both sides.
-5y = -2x - 3
Divide both sides by -5.
y = 2/5x + 3/5.
In order for the second line to be perpendicular to this line, the second line's slope must be -5/2 because 2/5 * -5/2 = -1.
2x + 5y = 4
Subtract 2x from both sides.
5y = -2x + 4
Divide both sides by 5.
y = -2/5x + 4/5
-2/5 * 2/5 = -4/10. That's not -1. The lines are not perpendicular.
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