The equation of a line passing through the point of the intersection of the lines $x - y + 1 = 0$ and $2x + 3y - 8 = 0$ and having x intercept $3$ is

The given lines are:

$x - y + 1 = 0$

$2x + 3y - 8 = 0$

From the first equation, $y = x + 1$. Substituting this into the second equation:

$2x + 3(x + 1) - 8 = 0$

$5x - 5 = 0 \Rightarrow x = 1$

Substituting $x = 1$ into $y = x + 1$, we get $y = 2$.

The point of intersection is $(1, 2)$.

The required line has an x-intercept of $3$, which means it passes through the point $(3, 0)$.

The equation of the line passing through $(1, 2)$ and $(3, 0)$ is given by:

$y - 0 = \dfrac{2 - 0}{1 - 3}(x - 3)$

$y = -1(x - 3)$

$x + y - 3 = 0$

Answer: $x + y - 3 = 0$