Give equations of four lines passing through the point $(-2, 4)$.

The general equation of a line passing through a point $(x_1, y_1)$ is given by $(y - y_1) = m(x - x_1)$,where $m$ is the slope.
For the point $(-2, 4)$,the equation is $(y - 4) = m(x + 2)$.
By choosing different values for the slope $m$,we can find infinitely many lines:
$1$. If $m = -1$,then $(y - 4) = -1(x + 2) \implies y - 4 = -x - 2 \implies x + y = 2$.
$2$. If $m = 1$,then $(y - 4) = 1(x + 2) \implies y - 4 = x + 2 \implies x - y = -6$.
$3$. If $m = -2$,then $(y - 4) = -2(x + 2) \implies y - 4 = -2x - 4 \implies 2x + y = 0$.
$4$. If $m = -0.5$,then $(y - 4) = -0.5(x + 2) \implies y - 4 = -0.5x - 1 \implies 0.5x + y = 3 \implies x + 2y = 6$.