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Step-by-step explanation:

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2x - 5y = 10

write in slope form, y = mx + b

5y = 2x - 10

y = 2/5x - 2

slope = 2/5

perpendicular slope = -5/2 (just the negative inverse of the slope)

then,

given coordinates are (3, -4)

y - y1 = m(x -x1)

y - (-4) = -5/2(x - 3)

y + 4 = -5/2x + 15/2

y = -5/2x + 7/2

2y = -5x + 7