Given:
The two points are (-1,10) and (2,4).
To find:
The equation of line which passes though the given points.
Solution:
If a line passes through two points, then the equation of line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The line passes through (-1,10) and (2,4). So, the equation of line is
[tex]y-10=\dfrac{4-10}{2-(-1)}(x-(-1))[/tex]
[tex]y-10=\dfrac{-6}{2+1}(x+1)[/tex]
[tex]y-10=\dfrac{-6}{3}(x+1)[/tex]
[tex]y-10=-2(x+1)[/tex]
Using distributive property, we get
[tex]y-10=-2x-2[/tex]
Adding 10 both sides, we get
[tex]y=-2x-2+10[/tex]
[tex]y=-2x+8[/tex]
Therefore, the required equation of line is [tex]y=-2x+8[/tex].
