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).