Respuesta :
Given:
A line passes through the points (2,-1) and (1,-5).
To find:
The equation of the line.
Solution:
If a line passes through the two points, then the equation of the line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The line passes through the points (2,-1) and (1,-5). So, the equation of the line is
[tex]y-(-1)=\dfrac{-5-(-1)}{1-2}(x-2)[/tex]
[tex]y+1=\dfrac{-5+1}{-1}(x-2)[/tex]
[tex]y+1=\dfrac{-4}{-1}(x-2)[/tex]
[tex]y+1=4(x-2)[/tex]
Using distributive property, we get
[tex]y+1=4(x)+4(-2)[/tex]
[tex]y+1=4x-8[/tex]
Subtract 1 from both sides.
[tex]y+1-1=4x-8-1[/tex]
[tex]y=4x-9[/tex]
Therefore, the correct option is B.
