Question

Bob plots the following data set on a graph [(0,10) , (5,25), (10,75) , (20,76) , (30,77), (50,78)]. He gets a straight line. What might Bob have done wrong?

Answer 1

He made the tick marks on each axis correspond to the values of the data points.

Answer 2

As we know to draw a straight line you need only two points. But as you have taken six points [(0,10) , (5,25), (10,75) , (20,76) , (30,77), (50,78)]. As this six points does not fall in a straight line i.e they are not collinear . So we will not get a straight line. To get a straight line if you join any two points out of these six points their slope must be equal.Let me explain you by giving an example

Consider points 1. (0, 10) and (5, 25) &2. (0, 10) and (10,75)

slope of line joining two points (x,y) and (p,q)=y-q/x-p

slope of 1 = 25-10/5-0=15/5 =3

slope of 2 =75-10/10-0 =85/10=8.5

So you will not get a straight line because in each case slope is not same. So to get a straight line bob must take ponts such that ratio of difference of X Coordinates to difference of Y coordinates must be same. For example [(5,10) ,(10,20) ,(15,30) ,(20,40)}. Bob as you will see if you take any two points out of these six points slopes are equal. So you must take points like this.