Question 363034: Are the points (-1,8), (1,2), and (4,-7) on the same line? Explain your reasoning
Found 2 solutions by mananth, Edwin McCravy:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! Are the points (-1,8), (1,2), and (4,-7) on the same line? Explain your reasoning
...
find the slope of the line passing through (-1,8) (1,2)
m=2-8/1-(-1)
=-6/2
=-3
...
form an equation using (-1,8). If the other two points satisfy the equation then all points are collinear.
y-8=-3(x-(-1)
y-8=-3x-3
y=-3x-3+8
y=-3x+5
..
point 1,2
2=-3(1)+5
2=-3+5
2=2 ( TRUE)
point (4,-7)
-7=-3*4+5
-7=-12+5
-7=-7 (TRUE)
so the lines are collinear
...
m.ananth@hotmail.ca
Answer by Edwin McCravy(20086)  (Show Source):
You can put this solution on YOUR website!
First let's plot them to get a heuristic answer:
(-1,8), (1,2), and (4,-7)
Now let's get a ruler and see if they look like they are:
Yes they look like they do, but "looking and seeing" is not good enough
for mathematical purposes.
Another way, beside the way the other tutor showed you, to show it
mathematically is to get the equation of the line through two of them and
then to show that the third point satisfies the equation:
We find the slope of the line that goes through (-1,8) and (1,2):
Then we substitute in the point-slope formula:
Now we substitute the third point (4,-7) into that equation:
The third point, which was not used to find the equation of
the line, satisfies the equation, so all three points lie on
the same line.
Edwin
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