Answer:
n= -4
Step-by-step explanation:
First we have to find the equation of line which passes through (6,3) and (8,4).
Then we have to pass this line through the point (n , -2).
we know, equation of line passing through (x1,y1) and (x2,y2) is
![\frac{x-x1}{x1-x2}=\frac{y-y1}{y1-y2}](https://tex.z-dn.net/?f=%5Cfrac%7Bx-x1%7D%7Bx1-x2%7D%3D%5Cfrac%7By-y1%7D%7By1-y2%7D)
So, the equation of line passing through (6,3) and (8,4) is
![\frac{x-6}{6-8}=\frac{y-3}{3-4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx-6%7D%7B6-8%7D%3D%5Cfrac%7By-3%7D%7B3-4%7D)
or, ![\frac{x-6}{-2} =\frac{y-3}{-1}](https://tex.z-dn.net/?f=%5Cfrac%7Bx-6%7D%7B-2%7D%20%3D%5Cfrac%7By-3%7D%7B-1%7D)
multiplying both sides by -2
x-6=2(y-3)
or, x-6=2y-6
or, x-2y=6-6
or, x-2y=0
Now, we have to pass this line through (n,-2)
So, using the point in the line, that is using x=n , y=-2
we get
n-2(-2)=0
or, n+4=0
or, n=-4