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

$3 x+4(m x+1)=9$

$x=\frac{5}{3+4m}$

As x is an integer, $3 + 4m_{ }$ must be a divisor of 5

SO $3+4m=\pm 1\text{ or }\pm 5$

(considering the integer value only)