Equation of a line joining two points $$\left(x_1, x_2\right) \&\left(y_1, y_2\right)$$ is $$\left(y-y_1\right)=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$$

Using the above formula, the equation of line joining points $$(2,4) \&(5,3)$$ is $$(y-4)=\frac{3-4}{5-2}(x-2)$$ which when simplified we get $$3 y+x=14$$

The $$y$$-intercept is a value of $$y$$ when $x$ is zero or we can say $$y$$-intercept is a point where line cuts y -axis.

So, the $$y$$-intercept of the line $$3 y+x=14$$ is $$3 y+0=14 \Rightarrow y=\frac{14}{3}$$

Hence the answer is (C).