SOLUTION: Find the distance of the line 8x-5y-15=0 from the point (-3,2)

You want to find the length of the green line.

The distance from the point (x1,y1)
to the line Ax+By+C=0 is given by this formula:
d = 

Plug in the formula and simplify. 

Edwin

There is a remarkable formula to calculate the distance from a given point to a given straight line in a coordinate plane.


    Let the straight line in a coordinate plane is defined in terms of its linear equation 

         a*x + b*y + c = 0,

    where "a", "b" and "c" are real numbers, and let P = (,) be the point in the coordinate plane. 

    Then the distance from the point P to the straight line is equal to

        d = .


Regarding this formula, see the lesson
    The distance from a point to a straight line in a coordinate plane
in this site.


Your straight line is 8x - 5y - 15 = 0.


So, the numbers in your case are  a= 8, b= -5, c= -15,   = -3,  = 2.


Substitute the given data  a= 8, b= -5, c= -15,   = -3,  = 2  into the formula to get the distance under the question


     =  =  =  = 5.194  (rounded).


Answer.  The distance is   =  = 5.194  (rounded).