Given:
A line contains the points R(-1, 8), S(1, 4) and T(6, y).
To find:
The value of y.
Solution:
Three points are collinear if:
[tex]x_1(y_2-y_3)+x_2(y_3-y_2)+x_3(y_1-y_2)=0[/tex]
A line contains the points R(-1, 8), S(1, 4) and T(6, y). It means, these points are collinear.
[tex]-1(4-y)+1(y-8)+6(8-4)=0[/tex]
[tex]-4+y+y-8+48-24=0[/tex]
[tex]2y+12=0[/tex]
Subtract 12 from both sides.
[tex]2y=-12[/tex]
Divide both sides by 2.
[tex]y=\dfrac{-12}{2}[/tex]
[tex]y=-6[/tex]
Therefore, the value of y is -6.
