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Answer:

5x -3y + 11 = 0 .

Step-by-step explanation:

Firstly let's find the slope of the line by converting the equation into slope intercept form as ,

=> 3x +5y = 7

=> 5y = 7 - 3x

=> y = (7-3x)/5

=> y = -3/5x + 7/5

  • On comparing this equation to the slope intercept form y = mx + c ,

=> m = -⅗

Now the slope of the line perpendicular to this line will be , say m'

=> m' =- 1/m

=> m' = -1/-⅗

=> m = 5/3

  • Now the line passes through (-1,2 ) . so on using point slope form , we get ,

=> ( x - x1) m = ( y - y1)

=> ( x - (-1)) × 5/3 = y - 2

=> ( x +1)×5 = 3( y -2)

=> 5x + 5 = 3y -6

=> 5x - 3y +5 +6=0

=> 5x -3y +11 = 0

• Hence the equation of line perpendicular to the given line is 5x -3y + 11 = 0 .

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