Question

Which pairs of points would result in a line with a rate of change of 2:1? Select all that apply.

A. ( − 4 , − 11 ) and ( − 2 , − 7 )
B. ( 5 , 6 )nd ( − 5 , 12 )
C. ( 0 , − 3 ) and ( − 4 , − 11 )
D. ( 0 , − 3 ) and ( 5 , 7 ) =

Answer 1

A, C and D

Explanation:

Let us find the slope(rate of change ) of each pair of points

The slope formula is

`m = (y_2-y_1)/(x_2-x_1)`

Plug in the points (− 4 ,− 11 ) and (-2 , − 7) to get;

`m = ( - 7 - - 11)/( - 2 - - 4) = (4)/(2) = (2)/(1)`

The rate of change of this pair 2:1

For B part, we plug the points ( 5 , 6 ) and ( − 5 , 12 )

`m = (12 - 6)/( - 5 - 12) = (6)/( - 10) = - (3)/(5)`

The rate of change is NOT 2:1

For part C, we plug in ( 0 , − 3 ) and ( − 4 , − 11 )

`m = ( - 11 - - 3)/( - 4 - 0) = ( - 8)/( - 4) = (2)/(1)`

The rate of change of this pair is also 2:1

For part D, we plug in (0 , − 3) and ( 5 , 7 )

`m = (7 - - 3 )/(5 - 0) = (10)/(5) = (2)/(1)`

This also has rate of change to be 2:1