Greatest number of the ordered pairs

Question

Each pair of X and Y values in the table are an ordered pair

 

X:1,2,3,4,5,6

Y:4,8,10,16,20,26

 

List the greatest number of the ordered pairs from the table that would lie on the same line if graphed on a coordinate plane

Answer 1

Start by looking at the relationship between the pairs.

 

If (1,4) and (2,8) are on the same line, then what will the Y values on that line be for the values of X = 3 thru 6?

 

(3, __)

(4, __)

(5, __)

(6, __)

 

You can actually fill them in by using basic addition.  Every time we move right by 1 X, we move up by the difference between Y1 and Y2 (8 - 4 => 4)

 

If there are at least 3 points from the list on that line, out of 6 points total, then the number of points on that line must be the greatest number of ordered pairs.  So list them.

 

If none of the other points are on that line, then do the same test for the points where X=1 and 3, then X=1 and 4, then X=1 and 5, and so on, until you find a line with at least three points on it.

 

If none of the lines with X=1 have three points, then do X=2 and 3, 2 and 4, 2 and 5, 2 and 6, 3 and 4, 3 and 5 etc, until you've checked all the combinations.

 

Here's me doing points 2 and 3 for you

 

(1, 4)  can't be in list because we already checked that line

(2, 8)  on this line 

(3, 10) on this line

(4, 12) not in list

(5, 14) not in list

(6, 18) not in list

 

If none of the lines have more than two points, then go back to the first line and two is the maximum number.