A line passes through (9,3),(12,4), and (n,-5) Find the value of n.

Given that a line passes through the points (9, 3), (12, 4), and (n, -5).
First we find the equation of the line that. passes through the points (9,3), and (12,4).
The equation of a line passing through the points $(x_1,y_1),(x_2,y_2)$ is
$\frac{y-y_1}{x-x_1}=\frac{y_1-y_2}{x_1-x_2}$
In this problem $(x_1,y_1)=(9,3),and(x_2,y_2)=(12,4).$
This implies that $x_1=9,y_1=3,x_2=12,y_2=4$
. Plugging these values $\in \frac{y-y_1}{x-x_1}=\frac{y_1-y_2}{x_1-x_2}$ we get the equation of the line is
$\in \frac{y-y_1}{x-x_1}=\frac{y_1-y_2}{x_1-x_2}$
$\Rightarrow \frac{y-3}{x-9}=\frac{3-4}{9-12}$
$\Rightarrow \frac{y-3}{x-9}=\frac{1}{3}$
$\Rightarrow 3(y-3)=x-9$
$\Rightarrow 3y-9=x-9$
$\Rightarrow x-3y=0$
Therefore, the equation of the line is $x-3y=0$
Also given that the line passing through the point $(n,-5)$
Putting $x=n,andy=-5$ in the equation of the line we get
$x-3y=0$
$\Rightarrow n-3(-5)=0$
$\Rightarrow n+15=0$
$\Rightarrow n=-15$
Thus, the value of n is -15,