The number of integral values of $m$ so that the abscissa of point of intersection of lines

$3 x+4 y=9$

$y=m x+1$

$\Rightarrow 3 x+4 m x+4=9$

$\Rightarrow(3+4 m) x=5$

$\Rightarrow x$ will be an integer when

$3+4 m=5,-5,1,-1$

$\Rightarrow \mathrm{m}=\frac{1}{2},-2,-\frac{1}{2},-1$

so, number of integral values of $m$ is 2