Question

Find the rate of change for each set of ordered pairs. What is the average rate of change of all the sets?

Answer 1

Answer: The answer is
`-(2)/(3).`

Step-by-step explanation: Let the Pairs of given points be

(i) A(-1,12) and B(6,26),

(ii) C(-1,-9) and D(3,3),

(iii) E(12,6) and F(11,13).

Now, the rate of change for pair (i) is given by

`R_1=(26-12)/(6-(-1))=(14)/(7)=2.`

Rate of change for pair (ii) is given by

`R_2=(3-(-9))/(3-(-1))=(12)/(4)=3.`

Rate of change for pair (iii) is given by

`R_3=(13-6)/(11-12)=(7)/(-1)=-7.`

Therefore, the average rate of change for all the sets is

`R=(R_1+R_2+R_3)/(3)=(2+3-7)/(3)=-(2)/(3).`

Thus, the answer is
`-(2)/(3).`

Answer 2

Rate of change for two ordered -pairs i,e
`(x_1, y_1)` and
`(x_2, y_2)` is given by;

`\text{Rate of change} = (y_2-y_1)/(x_2-x_1)`

1.

(-1, 12) and (6, 26)

Then;

`\text{Rate of change} = (26-12)/(6-(-1))`

or

`\text{Rate of change}(A) = (14)/(7) =2`

2.

(-1, -9) and (3, 3)

Then;

`\text{Rate of change} = (3-(-9))/(3-(-1))`

or

`\text{Rate of change}(B) = (12)/(4) =3`

3.

(12, 6) and (11, 13)

Then;

`\text{Rate of change} = (13-6)/(11-12)`

or

`\text{Rate of change}(C) = (7)/(-1) =-7`

Now, find the average rate of change of all the sets:

Average defined as the sum of all the observation to the number of observation.

`\text{Average rate of change of all sets} =(A+B+C)/(3) =(2+3-7)/(3) = -(2)/(3)`