Question 1179373
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                It can be done in different ways.


                I will show and explain one of them to you,  the most simplest,

                which you can,  probably,  will remember and understand all your life.



<pre>
You have two vectors with components


    (4-(-2), 1 - 5) = (6,-4)    (starts at (-2,5),  ends at (4,1) )

and

    (x-4,y-1)                   (starts at (4,1);  ends at (x,y) )



        You want these two vectors be parallel (or antiparallel, does not matter).



It means that the determinant, composed of the components of these vectors is equal to zero


    det {{{(matrix(2,2, x-4, y-1,  6,-4))}}} = 0.                <U>ANSWER</U>


It is your equation, same as


    -4*(x-4) - 6*(y-1) = 0.     (*)      <U>ANSWER</U>


You can simplify the resulting equation (*) any way as you want.
</pre>

Solved, explained and completed.