How do u determine if a set of points is on a line or not?

Question

if u are already given one set of points .

Answer 1

using two of the set, you can determine the y-intercept form of the line. Then if you plug any of the other points into the y-intercept equation and it is true, that point is on the line.

For example:

given 2 points (2,1) and (3,6) we can determine the slope (rise over run) as:

rise = y2-y1 = 6-1 = 5
run = x2-x1 = 3-2 = 1
slope = 5/1 = 5

slop-intercept equation is: y = mx + b where m=slope and b=y-intercept (where x = 0)

so y = 5x + b... and we can plug either point in for x and y to determine b:

1 = 5(2) + b
1 = 10 + b
b = -9

so...

y = 5x - 9

Now we can take any other point and plug it into this equation to check it the point is on the line. Let's try point (10,20):

20 = 5(10) -9
20 = 50 - 9
20 = 41

so we know point (10,20) does not lie on the same line as the other two points.

Another perhaps easier way to determine if a set of points lies on the same line is to simply start with two points (as above) and determine the slope (rise over run), then see if any of the other points in the set fall on the line by checking the slope (i.e. check the slope between one of the first two points and the unknown point). If they have the same slope, they are on the line!

Hope this helps (and makes sense)! ;)

Answer 2

Two points will always be in a line

Answer 3

Try graphing them and check it out.