Give the equations of four lines passing through $(2,3)$.

The equation of a line passing through a point $(x_1, y_1)$ can be represented in the form $a(x - x_1) + b(y - y_1) = 0$. Since there are infinitely many lines passing through a single point $(2, 3)$,we can choose different values for the coefficients $a$ and $b$ to generate them.
$1$. For $a=1, b=1$: $(x - 2) + (y - 3) = 0 \implies x + y = 5$.
$2$. For $a=3, b=-2$: $3(x - 2) - 2(y - 3) = 0 \implies 3x - 6 - 2y + 6 = 0 \implies 3x - 2y = 0$.
$3$. For $a=5, b=-3$: $5(x - 2) - 3(y - 3) = 0 \implies 5x - 10 - 3y + 9 = 0 \implies 5x - 3y = 1$.
$4$. For $a=2, b=3$: $2(x - 2) + 3(y - 3) = 0 \implies 2x - 4 + 3y - 9 = 0 \implies 2x + 3y = 13$.