Given:
Consider the two points are A(1,1) and B(0,5).
To find:
The equation of the line AB.
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]
We A(1,1) and B(0,5). So, the equation of line AB is:
[tex]y-1=\dfrac{5-1}{0-1}(x-1)[/tex]
[tex]y-1=\dfrac{4}{-1}(x-1)[/tex]
[tex]y-1=-4(x-1)[/tex]
[tex]y-1=-4x+4[/tex]
Add 1 on both sides, we get
[tex]y=-4x+4+1[/tex]
[tex]y=-4x+5[/tex]
Therefore, the equation of the line AB is [tex]y=-4x+5[/tex].
