Answer:
We get value of n=7
Step-by-step explanation:
If points lie on same line, they have same slope.
First we will find slope of points (3,5), (−1,3)
Using formula: ![Slope=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=Slope%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
We have ![x_1=3, y_1=5, x_2=-1, y_2=3](https://tex.z-dn.net/?f=x_1%3D3%2C%20y_1%3D5%2C%20x_2%3D-1%2C%20y_2%3D3)
Finding slope
![Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{3-5}{-1-3} \\Slope=\frac{-2}{-4} \\Slope=\frac{1}{2}](https://tex.z-dn.net/?f=Slope%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5CSlope%3D%5Cfrac%7B3-5%7D%7B-1-3%7D%20%5C%5CSlope%3D%5Cfrac%7B-2%7D%7B-4%7D%20%5C%5CSlope%3D%5Cfrac%7B1%7D%7B2%7D)
Using slope 1/2 and points (−1,3), and (7,n) we can find value of n
![Slope=\frac{y_2-y_1}{x_2-x_1}\\\frac{1}{2} =\frac{n-3}{7-(-1)} \\\frac{1}{2} =\frac{n-3}{7+1} \\\frac{1}{2} =\frac{n-3}{8}\\Cross\:Multiply\\1(8)=2(n-3)\\8=2n-6\\2n=8+6\\2n=14\\n=\frac{14}{2}\\n=7](https://tex.z-dn.net/?f=Slope%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%5Cfrac%7B1%7D%7B2%7D%20%3D%5Cfrac%7Bn-3%7D%7B7-%28-1%29%7D%20%20%5C%5C%5Cfrac%7B1%7D%7B2%7D%20%3D%5Cfrac%7Bn-3%7D%7B7%2B1%7D%20%5C%5C%5Cfrac%7B1%7D%7B2%7D%20%3D%5Cfrac%7Bn-3%7D%7B8%7D%5C%5CCross%5C%3AMultiply%5C%5C1%288%29%3D2%28n-3%29%5C%5C8%3D2n-6%5C%5C2n%3D8%2B6%5C%5C2n%3D14%5C%5Cn%3D%5Cfrac%7B14%7D%7B2%7D%5C%5Cn%3D7)
So, we get value of n=7