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:

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

$\text{Rate of change} = \frac{y_2-y_1}{x_2-x_1}$

1.

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

Then;

$\text{Rate of change} = \frac{26-12}{6-(-1)}$

or

$\text{Rate of change}(A) = \frac{14}{7} =2$

2.

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

Then;

$\text{Rate of change} = \frac{3-(-9)}{3-(-1)}$

or

$\text{Rate of change}(B) = \frac{12}{4} =3$

3.

(12, 6) and (11, 13)

Then;

$\text{Rate of change} = \frac{13-6}{11-12}$

or

$\text{Rate of change}(C) = \frac{7}{-1} =-7$

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.

$\text{Average rate of change of all sets} =\frac{A+B+C}{3} =\frac{2+3-7}{3} = -\frac{2}{3}$

Answer 2

Answer:  The answer is $-\dfrac{2}{3}.$

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

$R_1=\dfrac{26-12}{6-(-1)}=\dfrac{14}{7}=2.$

Rate of change for pair (ii) is given by

$R_2=\dfrac{3-(-9)}{3-(-1)}=\dfrac{12}{4}=3.$

Rate of change for pair (iii) is given by

$R_3=\dfrac{13-6}{11-12}=\dfrac{7}{-1}=-7.$

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

$R=\dfrac{R_1+R_2+R_3}{3}=\dfrac{2+3-7}{3}=-\dfrac{2}{3}.$

Thus, the answer is $-\dfrac{2}{3}.$