# Find an equation of the line which passes through the point (2, 1) and which is perpendicular to 3x+5y=11.

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Expert Answers

justaguide | Certified Educator

The equation of the line AB is 3x + 5y = 11. Convert this to the form y = mx + c where m is the slope of the line

3x + 5y = 11

=> 5y = -3x + 11

=> y = `(-3/5)x + 11/5`

A line perpendicular to this line has the slope `-1/(-3/5) = 5/3`

As the line passes through the point (2 , 1)

`(y - 1)/(x - 2 ) = 5/3`

=> 3y - 3 = 5x - 10

=> 5x - 3y - 7 = 0

**The equation of a line perpendicular to 3x + 5y = 11 and passing through (2, 1) is 5x - 3y - 7 = 0**