Find the equation of a line passing through the point (-2, 3) and having x-intercept 4 units.

Since, x-intercept = 4, it means line will intersect x-axis at (4, 0).

Since, line passes through (-2, 3) and (4, 0) so by two-point formula, equation is,

$y - y$1 = \dfrac{y2 - y1}{x2 - x1}(x - x1)

Putting values in above equation we get,

$\Rightarrow y - 3 = \dfrac{0 - 3}{4 - (-2)}(x - (-2)) \\[1em] \Rightarrow y - 3 = \dfrac{-3}{6}(x + 2) \\[1em] \Rightarrow y - 3 = \dfrac{-1}{2}(x + 2) \\[1em] \Rightarrow 2(y - 3) = -x - 2 \\[1em] \Rightarrow 2y - 6 = -x - 2 \\[1em] \Rightarrow 2y + x - 6 + 2 = 0 \\[1em] \Rightarrow x + 2y - 4 = 0.$

Hence, the equation of the line is x + 2y - 4 = 0.