Rate of ChangeDetermining Rate of Change/Slope from Tables, Graphs, Equation, and

Verbal Descriptions

Rate of Change

Directions: On the following slide, copy the equations into your notebook and and record the correct letter and ROC next to

the equation.

Match the Equation With Its ROC

Equations:1. Y = 3x – 52. Y = 9 + 12x3. -6x + 7 = Y4. Y = ½ x + 45. Y = ¾ x

ROC:

a. -12 h. 5b. 7

i. 3/4c. ½ j. 9d. 3

k. 12e. 4 f. Xg. -6

Matching Answers

Equations:1. Y = 3x – 5 d.2. Y = 9 + 12x k.3. -6x + 7 = Y g.4. Y = ½ x + 4 c.5. Y = ¾ x i.

ROC:

a. -12 h. 5b. 7

i. 3/4c. ½ j. 9d. 3

k. 12e. 4 f. Xg. -6

ROC and Tables

• Copy the tables into your notebook and determine the ROCs (ex. 3 apple per dollar).

6. 7.8.

Hours Miles

0 0

1 65

2 130

3 195

4 260

Months Balance ($)

0 7500

1 6700

2 5900

3 5100

4 4300

Movies Rented

Cost $

0 12

1 15

2 183 21

Answers: ROC and Tables• Copy the tables into your notebook and determine the ROCs (ex. 3 apple

per dollar).6. 7.

8.

65 miles per hour -$800 per month $ 4 per movie

Hours Miles

0 0

1 65

2 130

3 195

4 260

Months Balance ($)

0 7500

1 6700

2 5900

3 5100

4 4300

Movies Rented

Cost $

0 12

1 16

2 203 24

Graphs and ROCs• 9. Determine the ROC between the 2 points. Record in your notebook under

graphs.

(0,1)

(4,9)

Graphs and ROCs• 9. Determine the ROC between the 2 points.

(0,1)

(4,9)

Up 8 units

Over 4 units

ROC :8/4 = 2/1 or 2

Graphs and ROCs• 10. The Beats (headphones) cost $90 and are being paid off in monthly

installments. What is the ROC?

Cost of Beats ($)

Months

Graphs and ROCs• 10. The Beats cost $90 and are being paid off in monthly installment. What is the

ROC? (How much will be paid off each month?)

Cost of Beats ($)

Months

Rise: -$90

Run: 9 monthsROC: -$90/ 9 months= -$10 per month

$10 per month is paid

Copy these situations into your notebook and underline the rate of change for each.

11. Madi’s has 9 eggs. Her hens lay an average of 4 eggs per day. 12. To belong to the health club, you must pay a sign-up fee of $15 plus $2 per visit.13. Jaylin bought a motor scooter for $ 1200. He sends the bank a payment of $250 per month.14. To use your cell phone in England the cellphone company charges $1 per minute plus a $40 fee.15. Shayla has a cookie company and has 25,000 boxes of cookies. She sells 800 boxes a week.

Copy these situations into your notebook and underline the rate of change for each.

11. Madi’s has 9 eggs. Her hens lay an average of 4 eggs per day. 12. To belong to the health club, you must pay a sign-up fee of $15 plus $2 per visit.13. Jaylin bought a motor scooter for $ 1200. He sends the bank a payment of $250 per month.14. To use your cell phone in England the cellphone company charges $1 per minute plus a $40 fee.15. Shayla has a cookie company and has 25,000 boxes of cookies. She sells 800 boxes a week.