Respuesta :
Answer:
A
Step-by-step explanation:
Calculate the slope m using the slope formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (4, 1) and (x₂, y₂ ) = (x, - 6)
m = [tex]\frac{-6-1}{x-4}[/tex] = 1
m = [tex]\frac{-7}{x-4}[/tex] = 1 ( cross- multiply )
x - 4 = - 7 ( add 4 to both sides )
x = - 3 → A
The value of 'x' is -3 and this can be determined by using the two point slope formula and also by using the given data.
Given :
- The points (4, 1) and (x, -6) lie on the same line.
- The slope of the line is 1.
When two points are given then to determine the slope of the given line below formula can be used:
[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the points on the same line.
Now, substitute the value of slope m and points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the above equation in order to determine the value of 'x'.
[tex]\rm 1 = \dfrac{-6-1}{x-4}[/tex]
x - 4 = -7
x = -3
So, the value of x is -3.
For more information, refer to the link given below:
https://brainly.com/question/18666670
