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
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
* 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
∴ [tex]m=\frac{x-4}{-6-1}[/tex]
∴ [tex]m=\frac{x-4}{-7}[/tex]
∵ The slope of the line is m = 1
∴ [tex]\frac{x-4}{-7}=1[/tex]
- By using cross multiplication
∴ x - 4 = -7 ⇒ add 4 to both sides
∴ x = -3
* The value of x is -3
