Answer:
The value of x is -3
Step-by-step explanation:
* Lets explain how to solve the problem
- The slope of a line that passes through points (x1 , y1) and (x2 , y2) is
![m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
* Lets solve the problem
∵ The points (4 , 1) and (x , -6) lie on the same line
∵ The slope of the line is 1
- Let the point (4 , 1) is (x1 , y1) and the point (x , -6) ix (x2 , y2)
∵ x1 = 4 , x2 = x and y1 = 1 , y2 = -6
∴ ![m=\frac{x-4}{-6-1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7Bx-4%7D%7B-6-1%7D)
∴ ![m=\frac{x-4}{-7}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7Bx-4%7D%7B-7%7D)
∵ The slope of the line is m = 1
∴ ![\frac{x-4}{-7}=1](https://tex.z-dn.net/?f=%5Cfrac%7Bx-4%7D%7B-7%7D%3D1)
- By using cross multiplication
∴ x - 4 = -7 ⇒ add 4 to both sides
∴ x = -3
* The value of x is -3