SOLUTION: Find k so that the line through (7,2k) and (4,-3) is parallel to the line through (1,k+1) and (3,5).

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Find k so that the line through (7,2k) and (4,-3) is parallel to the line through (1,k+1) and (3,5).      Log On


   

Question 1150510: Find k so that the line through (7,2k) and (4,-3) is parallel to the line through (1,k+1) and (3,5).
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

The slope of the first line is


    m1 = %28%28-3%29-2k%29%2F%284-7%29 = %282k%2B3%29%2F3.


The slope of the second line is


    m2 = %285-%28k%2B1%29%29%2F%283-1%29 = %284-k%29%2F2.


The line are parallel if and only if m1 = m2


    %282k%2B3%29%2F3 = %284-k%29%2F2.


To solve this equation, first cross-multiply; then simplify


    2*(2k+3) = 3*(4-k)

    4k + 6 = 12 - 3k

    4k + 3k = 12 - 6

    7k      = 6

     k      = 6%2F7.      ANSWER