Given the point $(1,\, 2)$, find the equation of a line on which it lies. How many such equations are there ?
Given the point $(1,\, 2)$, find the equation of a line on which it lies. How many such equations are there ?
Here $(1,\, 2)$ is a solution of a linear equation you are looking for. So, you are looking for any line passing through the point $(1,\, 2)$. One example of such a linear equation is $x + y = 3$. Others are $y -x = 1$, $y = 2x$, since they are also satisfied by the coordinates of the point $(1,\, 2)$. In fact, there are infinitely many linear equations which are satisfied by the coordinates of the point $(1,\, 2)$.
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