SOLUTION: {{{ find the value of k (9,-k) (3k,-1) m=-1/3}}} I know I need to use M=(y2-y1)/(x2-x1) but I'm stuck on the solution

Algebra ->  Linear-equations -> SOLUTION: {{{ find the value of k (9,-k) (3k,-1) m=-1/3}}} I know I need to use M=(y2-y1)/(x2-x1) but I'm stuck on the solution      Log On


   

Question 652931: +find+the+value+of+k+%289%2C-k%29+%283k%2C-1%29+m=-1%2F3 I know I need to use M=(y2-y1)/(x2-x1) but I'm stuck on the solution
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
find the value of k
(x1,y1=(9,-k) and
(x2,y2= (3k,-1)
m=-1%2F3 -slope (could be written as m=-0.333333

m=%28y2-y1%29%2F%28x2-x1%29

-1%2F3=%28-1-%28-k%29%29%2F%283k-9%29..cross multiply

-1%283k-9%29=%28-1%2Bk%293
-3k%2B9=-3%2B3k
9%2B3=3k%2B3k
12=6k
12%2F6=k
highlight%28k=2%29}
so, the points are (9,-2) and (6,-1)
now we can use these points to find equation of straight line given 2 points

Solved by pluggable solver: FIND EQUATION of straight line given 2 points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (9, -2) and (x2, y2) = (6, -1).
Slope a is .
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D, or -0.333333333333333%2A9+%2Bb+=+1. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D, or b=-2--0.333333333333333%2A9+=+1.

y=(-0.333333333333333)x + (1)

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