The number of integer value of m, for which the x-coordinate of the point of intersection of the lines 3x+4y = 9 and y = mx + 1 is also an integer is

x-coordinate of the point of intersection is given by

$\begin{array}{r}3\mathrm{x}+4(\mathrm{mx}+1)=9\\ \Rightarrow \mathrm{x}=\frac{5}{3+4\mathrm{m}}\end{array}$

As x is an integer, 3+4m must be a divisor of 5

$\begin{array}{l}\mathrm{so}, 3+4\mathrm{m}=\pm 1\text{ or }\pm 5\\ \Rightarrow \mathrm{m}=-1\text{ or }-2\end{array}$

(considering the integer value only)