Question

Find the value of K if the points (-2,3),(1,0) and (k,2) lie on the same line.

Answer 1

we need the slope of the line
the slope of the line between \((-2,3)\) and \((1,0)\) is \(m=\frac{3-0}{-2-1}=\frac{3}{-3}=-1\)

Answer 2

yes

Answer 3

this means for each unit increase in \(x\) there is a unit decrease in \(y\)

Answer 4

we see that \((-2,3)\) is on the line
one decrease in \(y\) gives \((k,2)\) and so \(x\) must have been increased by 1 unit from -2
therefore it is \((-1,2)\)

Answer 5

so you mean k is the answer from the slope?

Answer 6

we can also use algebra if that is too much thinking\frac{36m^4n^3}{24m^2n^5}
slope is \(-1\) and so we get the equation \[\frac{3-2}{-2-k}=-1\]
\[\frac{1}{-2-k}=-1\]
\[1=2+k\]
\[k=-1\]

Answer 7

k we can find from the slope since \(m=\frac{y_2-y_1}{x_2-x_1}=-1\)
use the points \((-2,3)\) and \((k,2)\) compute the slope, the result \(=-1\) and solve for \(k\)

Answer 8

i dont understand

Answer 9

i thought k=-1

Answer 10

yes, \(k=-1\) and also the slope is \(-1\) but that is a coincidence

Answer 11

thanks

Answer 12

yw

Answer 13

why you use -2,3 why not 1,0?

Answer 14

try it and you will see that it makes no difference at all

Answer 15

good question though! lets check

Answer 16

thanks

Answer 17

this is my review for my finals... I really appreciate your help

Answer 18

\[\frac{2-0}{k-1}=-1\]
\[\frac{2}{k-1}=-1\]
\[2=-1(k-1)\]
\[2=-k+1\]
\[1=-k\]
\[k=-1\] makes no difference which point you pick

Answer 19

no problem, glad to help

Answer 20

thanks a lot