Finding an equation form of a line from a matrix

Question

I have a matrix $$A = \begin{bmatrix} 25/26 & -5/25 \\ -5/26 & 1/26 \end{bmatrix}.$$

$A$ is a matrix for projection onto a line $L$ that goes through $(0,0)$.

I want to find an equation form of the line $L$. I know the line should be negative from reading the points.

However, I do not know how to find the slope of the line. Where should I begin?

Answer 1

The matrix $A$ has rank one (why?), so its image (column space) is spanned by any nonzero column. Since this image is a lone through the origin, this gives you a direction vector for the line.