Equation for a line through an origin

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The equation "-4*y + x = 0" is marked wrong by an automatic grader, likely due to expectations for a normalized vector or a positive coefficient for 'a'. There is no unique solution to the form "ay + bx = 0" since any multiple of a solution is also valid. The user suggests trying the equation "4*y - x = 0" with a positive 'a' instead. This indicates a need for clarity on the grading criteria for vector equations. The discussion highlights the importance of adhering to specific formatting and positivity in mathematical expressions.
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Homework Statement
Find the equation for the line through the origin that is perpendicular to the vector (-1,4). Enter the equation in the form: ##a*y+b*x=0##
Relevant Equations
Dot product of the vector (-1,4) and the vector parallel to the line has to be 0.
Why is this wrong?
$$-4*y+x=0$$

$$\vec (-1, 4)\cdot\vec (4,1)=0$$
 
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Why do you think it is wrong?
 
It has been marked as wrong by an automatic grader. But I don't understand why. :(
 
Poetria said:
It has been marked as wrong by an automatic grader. But I don't understand why. :(
There is no unique solution to ##ay+bx=0## because all ##acy+acx=0 \;(c\neq 0)## are solutions, too. Could be that whatever checked it expected a normalized vector, or a positive ##a##.
 
It is stated: expression in the form ##a*y+b*x##. I will try with the positive a then.

$$4*y-x=0$$

Many thanks. :)
 

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