Write the equation of the line perpendicular to the line 2x +5y =12 and passing through the point(-10,3)

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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If y=mx+c is straight line and y=m'x+c is another straight line they will be perpendicular when m*m' = -1


2x+5y = 12

      5y = 12-2x

        y = (-2/5)x+(12/5)


Lets say the line perpendicular to this line is y = mx+c

So according to the above theorem;

(-2/5)*m = -1

          m = 5/2


So we can write the perpendicular line as y = (5/2)x+c

Now it is given that this perpendicular line goes through point (-10,3).

3 = (5/2)*(-10)+c

c = 28


So the equation to the perpendicular line is y = (5/2)x+28