best explanation gets 10points. I want it in a clear format

Update:NEEDED IN STANDARD FORM

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Best answer

If two lines are perpendicular their slopes are negative reciprocals. First solve for y to get the slope of your line:

5x + 2y = 10 --> 2y = -5x + 10 --> y = - (5/2)x + 5

The slope of the new line is going to be 2/5 and it goes through (5, 5)

so we have y = (2/5)x + b

Now plug in your point (5, 5)

5 = (2/5)5 + b --> b = 3

So the equation of your new line is going to be:

y = (2/5)x + 3

now standard form:

-(2/5)x + y = 3

2x - 5y = -15 I multiplied both sides by -5

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First write the equation of the perpendicular graph in (y=mx+b) form

2y=-5x+10

y=-5/2+5

The slope is -5/2, Since it is the perpendicular the orginal graph will have the opposite slope

so the slope of the orginal graph is 2/5

y=2/5x+b

Plug in the x and y values in this equation

5=2/5*5+b

b=3

y=2x/5 +3

5y=2x+15

2x-5y+15=0