math - why we get only one unique straight line in a,b co ordinates for a point given in x,y co-ordinates? -

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if there point given in x,y co-ordinate, can pass infinite number of straight lines varying slope , intercept b. when fix our x , y , vary our , b in a,b co-ordinate single unique line. why? found annoying while studying hough transform.

i don't understand want ask....but yes may clear things bit. when fix point can make infinite lines pass through it.this obvious. fix a,b co-ordinates have fixed 1 particular case slope , y-intercept both.

now note slope can vary between definite range. if consider argument, vary 0 degrees 180 degrees. out of infinite lines having different slopes pass through point (in case point on y-axis i.e. y-intercept of line) selecting 1 line in particular having specific slope. 1 such line possible.

i hope answers question...


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