Is it necessary to rearrange the equation of a line so that it is in the $y=mx+b$ form before using substitution to check whether a point is on the line? If yes, why? If no, why?
2026-03-31 21:07:16.1774991236
Using substitution to determine if a given point is on the line
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No, you just need to ensure, upon substitution, that equality holds.
$$y = mx + b \iff y - mx = b \iff y - mx - b = 0 $$
If $(x_0, y_0)$ is a solution to any one of the above, it is a solution to all the equations above. It is also a solution to $y - y_0 = m(x - x_0)$
Adding/subtracting a term to/from each side of an equation doesn't change the equality, and multiplying/dividing the equation by a non-zero constant doesn't change the equality.
If you know $x= a$ but need to solve for $y$, then using the form $y = mx + b$ and substituting for $x$, gives you the value of $y$ most immediately. But given $x$, we can solve for $y$ no matter what form the equation of a line.