Question

Which of the ordered pairs forms a linear relationship: (-2,5) (-1,2) (0,1) (1,2)? Why?

Answer 1

P1 and P4 define a line segment with the same slope as the line segment defined by P2 and P3

Explanation:

To compare the possible slopes with 4 points, one should determine the slopes for P1P2, P1P3, P1P4, P2P3, P2P4 and P3P4.
To determine a slope defined by two points:
`k_(AB)=(Delta y)/(Delta x)=(y_B-Y_A)/(x_B-x_A)`

`k_(P1P2)=(2-5)/(-1+2)=-3/1=-3`
`k_(P1P3)=(1-5)/(0+2)=-4/2=-2`
`k_(P1P4)=(2-5)/(1+2)=-3/3=-1`
`k_(P2P3)=(1-2)/(0+1)=-1/1=-1`
`k_(P2P4)=(2-2)/(1+1)=0/2=0`
`k_(P3P4)=(2-1)/(1-0)=1/1=1`

`k_(P1P4)=k_(P2P3)` => segments P1P4 and P2P3 have the same slope