SOLUTION: Find an equation of the line in the form ax+by=c, where​ a, b, and c are integers with no factor common to all three and a>=0. The line with​ y-intercept 9 and perpendicular t

There is a standard procedure on how to construct an equation of a line perpendicular to a given line.



    This procedure is described in all details with examples in my lesson

        - Equation for a straight line perpendicular to a given line and passing through a given point 

    in this site, which I recommend you to read and to learn.



In this case this procedure works in this way:


    a)  take the form  "x + 5y" of the given equation of the given line.

    b)  in this form, swap the coefficients and change the sign at one of the coefficient, keeping the other coefficient with its original sign.

    c)  By doing in this way, yo will get the left side of the projected equation in the form

           "5x - y",

        so the future equation will take the form  

            5x - y = c,      (1)

        where " c " is some constant, now unknown.

    d)  To determine the constant " c " value, use the fact the the projected line passes through the point (x,y) = (0,9)

         and substitute these coordinates into equation (1).  It will give you

             c = 5x - y = 5*0 - 9 = -9.


    e)  Thus the final equation of the perpendicular line is

              5x - y = -9.


        It satisfies all requirements of the problem.