JEE Main 2021 (Online) 18th March Morning ShiftQuestion 1
The number of integral values of $m$ so that the abscissa of point of intersection of lines $3x+4y=9$ and $y=mx+1$ is also an integer, is :
Points and Straight Lines
Solution
$3x+4(mx+1)=9\Rightarrow x=\frac{5}{3+4m}$. Integer $x$ requires $3+4m\in\{\pm1,\pm5\}$: $m=-1\ (3+4m=-1)$, $m=-2\ (-5)$; $m=-\frac12,\frac12$ not integers. Two integral values. Option (C).