Question

use the concept of slope to find t such that three points are collinear
(-3,3) (t,-1) (8,6) i really dont understand this problem...step by step anyone?

Answer 1

you need so make sure the slopes are the same

Answer 2

the slope of the line between (-3,3) and (8,6) is
\[\frac{6-3}{8-(-3)}\]

\[=\frac{3}{11}\]

Answer 3

and so you have to make sure that
\[\frac{-1-3}{t-(-3)}=\frac{-4}{t+3}=\frac{3}{11}\]

Answer 4

you good from there?

Answer 5

yea and thats where i got stuck

Answer 6

oh ok

Answer 7

cross multiply to get
\[-44=3(t+3)\] how about now?

Answer 8

yes im following

Answer 9

\[-44=3t+9\]
\[-53=3t\]
\[t=-\frac{53}{3}\]hmm looks bad let me check

Answer 10

yea i think thats right. i understand it way better

Answer 11

thans!!!

Answer 12

you could also find the equation for the line, then replace y by -1

Answer 13

equation is
\[-3 x+11 y-42 = 0\]

Answer 14

let's see if it works

Answer 15

ok

Answer 16

\[-3x+11\times -1-42=0\]
\[-3x=53\] yes it works

Answer 17

whew i got nervous

Answer 18

so i could use both ways right?

Answer 19

sure your choice.
find the line, plug in the point
or make sure the slopes match up.

i think first way might be shorter because in both you still have to find the slope but in second way you also have to find the equation of the line

Answer 20

i mean "in the first way you still have to find the equation of the line"

Answer 21

oh ok thanks for your help!!