The area of the triangle formed by the line passing through the points  $(3,4),(5,6)$ with the coordinate axes is

Let $(x_1,y_1)=(3,4)$

Let $(x_2,y_2)=(5,6)$

Equation of two points is: $\frac{y-y_1}{y_1-y_2}=\frac{x-x_1}{x_1-x_2}$

$\frac{y-4}{4-6}=\frac{x-3}{3-5}$

$x-y+1=0$

$x-y=-1$

$\frac{x}{-1}+\frac{y}{1}=1$

Area of triangle  $=\frac{1}{2}\left|ab\right|$

$=\frac{1}{2}|-1\times 1|$

$=\frac{1}{2}\text{\hspace{0.17em}sq.units}$