Tuesday

September 1, 2015
Posted by **sally** on Sunday, January 27, 2013 at 5:20pm.

1- By trying to solve the problem using (y2-y1)/(x2-x1)=slope -- and then, find the (b) in y=mx+b for two points takes way way too long to be a 7th grade probem. My son has already been working on it for over two hours. There must be a shortcut…

2- Why is it that; y=mx+b for points with a zero never give the righ b? e.g. (0,3)

Problem:

The coordinates of the points are:

A= (0,3) | B=(2.11) | C=(3,-3) | D=(-1,9) | E=(-3,10) |F=(6,10) | G=(-5,19) | H=(-6,18)

Three, and only three of these points are collinear. The student’s task is to determine “Analytically” and without plotting, which three is the collinear trio.

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**sally**, Sunday, January 27, 2013 at 5:26pmsorry B=(-2,11)

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**Reiny**, Sunday, January 27, 2013 at 5:56pmI agree with you that this is a rather ridiculous question

There are 21 possible pairs of points, each pair could give us the equation of a line containing such a pair.

If the objective is to use the method you suggest, it could just as easily be effictive with , let's say, 4 points.

I would have allowed my students to make a sketch, thus eliminating some of the more obvious non-collinear points.

You don't actually have to find the equation of the line. If you find the slopes of pairs that have a common point, and those two slopes are equal, then the 3 points are collinear.

e.g. If slope PQ = slope PR , the P, Q, and R are collinear, notice P was the "link"

but, if slope PQ = slope RS, all we know is that PQ || RS

As to your point #2, I think you must be making some kind of error,

Using a point such as (0,3) in y=mx +b will let you find b in the same way as using any other point

e.g. suppose we know y = 4x + b and we are told that (0,3) is on it

3 = 4(0) + b

b = 3

notice that in y = mx + b, the b value is the y-inercept

and of course (0,3) is the point of the y-intercept, so obviously if in a point, the x = 0, the y must be the value of b in the equation.

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**Damon**, Sunday, January 27, 2013 at 6:15pmI played with this for a while but could see no practical way to do it without sketching the points.

I dis put the points in order of increasing x from -6 to +6 which makes it easier to visualize

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**sally**, Sunday, January 27, 2013 at 7:50pmThank you very much Reiny and also Damon. This is the first time I felt embarrassed helping my son. Sign of things to come of course. As Reiny suggested, we ended up plotting and then selecting less than half a dozen candidates. I also cheated and made a spreadsheet just to speed things up. The spreadsheet quickly showed the Trio is: C, H AND F.

Thank you again