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Rate of Change & Initial Value — Easy Worksheet 2
Grade 8 · MathSheets Name: ____________________ Date: __________
Answer each question. A rate of change is negative when the quantity decreases. Give numbers only, without units.
How to solve
The rate of change is how much y changes for each 1 unit of x: (change in y) ÷ (change in x). The initial value is the value of y when x = 0 (the starting amount or fixed fee). Together they give the linear model y = mx + b, where m is the rate of change and b is the initial value.
Example
A phone battery is at 90% and loses 7% every hour. What is the rate of change of the battery level in percent per hour?
Answer: -7
Not quite. The answer is
💡 It goes up by 4 each mile, so the rate of change is 4.
✓ Correct!
Not quite. The answer is
💡 It goes up by 4 each mile, so the rate of change is 4.
💡 How to solve: Rate of Change & Initial Value
The rate of change is how much y changes for each 1 unit of x: (change in y) ÷ (change in x). The initial value is the value of y when x = 0 (the starting amount or fixed fee). Together they give the linear model y = mx + b, where m is the rate of change and b is the initial value.
Try a similar one
A tank holds 388 liters of water and drains 8 liters every minute. What is the rate of change of the water left in liters per minute?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Start at 3 and add 2 for each of the 6 miles: 3 + 2 × 6 = 3 + 12 = 15. The answer is 15.
✓ Correct!
Not quite. The answer is
💡 Start at 3 and add 2 for each of the 6 miles: 3 + 2 × 6 = 3 + 12 = 15. The answer is 15.
💡 How to solve: Rate of Change & Initial Value
The rate of change is how much y changes for each 1 unit of x: (change in y) ÷ (change in x). The initial value is the value of y when x = 0 (the starting amount or fixed fee). Together they give the linear model y = mx + b, where m is the rate of change and b is the initial value.
Try a similar one
A phone battery is at 92% and loses 10% every hour. What is the rate of change of the battery level in percent per hour?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Rate of change = (change in y) ÷ (change in x) = (24 − 27) ÷ (7 − 4) = −3 ÷ 3 = −1.
✓ Correct!
Not quite. The answer is
💡 Rate of change = (change in y) ÷ (change in x) = (24 − 27) ÷ (7 − 4) = −3 ÷ 3 = −1.
💡 How to solve: Rate of Change & Initial Value
The rate of change is how much y changes for each 1 unit of x: (change in y) ÷ (change in x). The initial value is the value of y when x = 0 (the starting amount or fixed fee). Together they give the linear model y = mx + b, where m is the rate of change and b is the initial value.
Try a similar one
A taxi ride costs $6 plus $2 per mile. What is the rate of change of the fare in dollars per mile?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The starting amount, when x = 0, is 37, so the initial value is 37.
✓ Correct!
Not quite. The answer is
💡 The starting amount, when x = 0, is 37, so the initial value is 37.
💡 How to solve: Rate of Change & Initial Value
The rate of change is how much y changes for each 1 unit of x: (change in y) ÷ (change in x). The initial value is the value of y when x = 0 (the starting amount or fixed fee). Together they give the linear model y = mx + b, where m is the rate of change and b is the initial value.
Try a similar one
A taxi ride costs $9 plus $2 per mile. What is the rate of change of the fare in dollars per mile?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 It goes up by 41 each month, so the rate of change is 41.
✓ Correct!
Not quite. The answer is
💡 It goes up by 41 each month, so the rate of change is 41.
💡 How to solve: Rate of Change & Initial Value
The rate of change is how much y changes for each 1 unit of x: (change in y) ÷ (change in x). The initial value is the value of y when x = 0 (the starting amount or fixed fee). Together they give the linear model y = mx + b, where m is the rate of change and b is the initial value.
Try a similar one
A gym charges a $85 sign-up fee plus $28 per month. What is the rate of change of the total cost in dollars per month?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Start at 32 and subtract 2 for each of the 5 hours: 32 − 2 × 5 = 32 − 10 = 22. The answer is 22.
✓ Correct!
Not quite. The answer is
💡 Start at 32 and subtract 2 for each of the 5 hours: 32 − 2 × 5 = 32 − 10 = 22. The answer is 22.
💡 How to solve: Rate of Change & Initial Value
The rate of change is how much y changes for each 1 unit of x: (change in y) ÷ (change in x). The initial value is the value of y when x = 0 (the starting amount or fixed fee). Together they give the linear model y = mx + b, where m is the rate of change and b is the initial value.
Try a similar one
Sam has $107 saved and adds $7 every week. What is the rate of change of the amount he has saved in dollars per week?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Rate of change = (change in y) ÷ (change in x) = (73 − 85) ÷ (3 − 1) = −12 ÷ 2 = −6.
✓ Correct!
Not quite. The answer is
💡 Rate of change = (change in y) ÷ (change in x) = (73 − 85) ÷ (3 − 1) = −12 ÷ 2 = −6.
💡 How to solve: Rate of Change & Initial Value
The rate of change is how much y changes for each 1 unit of x: (change in y) ÷ (change in x). The initial value is the value of y when x = 0 (the starting amount or fixed fee). Together they give the linear model y = mx + b, where m is the rate of change and b is the initial value.
Try a similar one
A taxi ride costs $9 plus $4 per mile. What is the rate of change of the fare in dollars per mile?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The starting amount, when x = 0, is 35, so the initial value is 35.
✓ Correct!
Not quite. The answer is
💡 The starting amount, when x = 0, is 35, so the initial value is 35.
💡 How to solve: Rate of Change & Initial Value
The rate of change is how much y changes for each 1 unit of x: (change in y) ÷ (change in x). The initial value is the value of y when x = 0 (the starting amount or fixed fee). Together they give the linear model y = mx + b, where m is the rate of change and b is the initial value.
Try a similar one
A phone battery is at 93% and loses 3% every hour. What is the rate of change of the battery level in percent per hour?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Rate of Change & Initial Value — Easy Worksheet 2
Answer each question. A rate of change is negative when the quantity decreases. Give numbers only, without units.