10. What is the equation of the line perpendicular
to 2x + 5y = 20 and containing the point
(10,4)?

Hi ,  

1 step : you must isolate the   "y"  and have a  line in reduce  form.

so  :   A )  2x+5y =20  

               5y =  20-2x

                 5y = -2x+20

                   y =  -2/5 X + 20/5

                   y = -2/5 X +4

Now we must find the equation of the second line.  Let call it  " B"  

The B equation would be a line, and so written in the form of  :  

y = mx +p  

The trick is :    the product of    "m" from "A" and  "m" from b must be  : -1  

let call  "m"  from b :   m(b)

so :   -2/5 * m(b) = -1

                 m(b) = -1 / -2/5  =  -1 *  5/ -2  =   - 5/-2  = 5/2

Now we now that  m(b) is  5/2   and  your   B line  pass through  

by point  :   (10 ; 4)  

so :   5/2 (10) + b = 4

         50/2 + b = 4

          25 +b = 4

             b =  4-25

              b =  -21  

so the equation of  B  is  :   y = 5/2 X -21

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