Question

A line contains the points R (-1, 8) S (1, 4) and T (6, y). Solve for y. Be sure to show and explain all work.

Answer 1

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:

$x_1(y_2-y_3)+x_2(y_3-y_2)+x_3(y_1-y_2)=0$

A line contains the points R(-1, 8), S(1, 4) and T(6, y). It means, these points are collinear.

$-1(4-y)+1(y-8)+6(8-4)=0$

$-4+y+y-8+48-24=0$

$2y+12=0$

Subtract 12 from both sides.

$2y=-12$

Divide both sides by 2.

$y=\dfrac{-12}{2}$

$y=-6$

Therefore, the value of y is -6.