SOLUTION: let A=(6,-4) and B=(-2,-3) and C=(t, -8). find the value of t so that the point C lies on the same line as A and B

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: let A=(6,-4) and B=(-2,-3) and C=(t, -8). find the value of t so that the point C lies on the same line as A and B      Log On


   

Question 896247: let A=(6,-4) and B=(-2,-3) and C=(t, -8). find the value of t so that the point C lies on the same line as A and B
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Slope for AB,
%28-4-%28-3%29%29%2F6-%28-2%29%29=-1%2F8
Line AB would have y-intercept b=y-mx=-4-%28-1%2F8%29%2A6=-4%2B3%2F4=-16%2F4%2B3%2F4=-13%2F4;
Equation for line AB, highlight%28y=-%281%2F8%29x-13%2F4%29.

You want to know x when y=-8.
Solve the equation for x.

-x%2F8=y%2B13%2F4
x=%28y%2B13%2F4%29%2F%28-8%29
x=-y%2F8-13%2F32
Substitute for y.
x=-%28-8%29%2F8-13%2F32
x=1-13%2F32
x=%2832-13%29%2F32
highlight%28x=19%2F32%29, in this example, same as t.