SOLUTION: Points (1,3) (-4,7) and (-29, k) are collinear. Find k. So, I found the slope of the first two points they gave me, I just don't understand what to do with it from there.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Points (1,3) (-4,7) and (-29, k) are collinear. Find k. So, I found the slope of the first two points they gave me, I just don't understand what to do with it from there.      Log On


   

Question 997632: Points (1,3) (-4,7) and (-29, k) are collinear. Find k. So, I found the slope of the first two points they gave me, I just don't understand what to do with it from there.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Study this, and analyze what the outline of the method is:

m=%287-3%29%2F%28-4-1%29=4%2F-5=-%284%2F5%29

The point-slope form equation of a line, y-3=-%284%2F5%29%28x-1%29,
y-3=-4x%2F5%2B4%2F5
y=-4x%2F5%2B4%2F5%2B3
highlight_green%28y=-4x%2F5%2B3%264%2F5%29

Point (-29,k) is supposed to be on this line but k currently unknown, but can be found.
---redoing this part---

The point (-29,k) must satisfy the equation for the line.
k=-%284%28-29%29%2F5%29%2B3%264%2F5
k=%284%2A29%29%2F5%2B19%2F5
k=135%2F5
highlight%28k=27%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Points (1,3) (-4,7) and (-29, k) are collinear. Find k. So, I found the slope of the first two points they gave me, I just don't understand what to do with it from there.
Any 2 points will give you the same slope, since all points are collinear

m, or slope = %283+-+7%29%2F%281+-+-+4%29 --------> -+4%2F5

Therefore, %28k+-+7%29%2F%28-+29+-+-+4%29+=+-+4%2F5 -----> %28k+-+7%29%2F%28-+25%29+=+-+4%2F5

5(k - 7) = - 4(- 25) -------- Cross-multiplying

5k - 35 = 100

5k = 100 + 35

5k = 135

k = 135%2F5, or highlight_green%28k+=+27%29