SOLUTION: Find the value of y such that the points are collinear. (−6, −4), (0, y), (−3, −3)

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Question 1179372: Find the value of y such that the points are collinear.
(−6, −4), (0, y), (−3, −3)
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

find the value of y such that the points are collinear:
(-6, -4), (0,+y), (-3, -3)

the points are collinear if they lie on same line
y=mx%2Bb
use given points to calculate a slope m
(-6, -4) and (-3, -3)
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
m=%28-3-%28-4%29%29%2F%28-3-%28-6%29%29
m=%28-3%2B4%29%2F%28-3%2B6%29
m=1%2F3
y=%281%2F3%29x%2Bb...........use one point to calculate b

-3=%281%2F3%29%28-3%29%2Bb
-3=-1%2Bb
-3%2B1=b
b=-2
your equation is:

y=%281%2F3%29x-2
now we can find missing coordinate of the point (0,+y)

y=%281%2F3%29%2A0-2
y=-2

the point is (0,+-2)




Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Solving the problem using formal mathematics as the other tutor did is good practice in some basic algebra, involving the slope of a line.

But your understanding of math will be much stronger if, instead of plugging numbers into formulas, you UNDERSTAND what the formal mathematics is doing for you.

The three points are supposed to be collinear, meaning the slope between pairs of points is the same.
The informal definition of slope is "rise over run", or change in y divided by change in x.
Arranged left to right, the three points are (-6,-4), (-3,-3), and (0,y).
From the first point to the second, the run is 3 (from -6 to -3) and the rise is 1 (from -4 to -3).
From the second point to the third, the run is also 3 (from -3 to 0); since the slopes are the same, the rise has to be 1.
A rise of 1 from y=-3 puts you at y=-2.

ANSWER: at x=0, y is -2.