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Interpreting Rate of Change & Initial Value — Easy Worksheet 2
Grade 8 · Whoobee Name: ____________________ Date: __________
Answer each question with "rate of change" or "initial value".
How to solve
In a linear model y = mx + b, the number multiplied by the input variable (m) is the rate of change: how much the output goes up or down for each 1 unit of the input. The number on its own (b) is the initial value: the output when the input is 0, such as a starting amount or a fixed fee. The order of the terms does not matter, so in 40 + 15h the 15 is still the rate of change. A minus sign in front of the rate means the amount goes down.
Example
The equation C = 28h + 32 gives the cost C, in dollars, of renting a boat for h hours. What does the number 28 represent: the rate of change or the initial value?
Answer: rate of change
Not quite. The answer is
💡 25 is the number multiplied by t, so it tells how much W changes for each 1 unit of t: the hose adds 25 liters each minute. It is the rate of change.
✓ Correct!
Not quite. The answer is
💡 25 is the number multiplied by t, so it tells how much W changes for each 1 unit of t: the hose adds 25 liters each minute. It is the rate of change.
💡 How to solve: Interpreting Rate of Change & Initial Value
In a linear model y = mx + b, the number multiplied by the input variable (m) is the rate of change: how much the output goes up or down for each 1 unit of the input. The number on its own (b) is the initial value: the output when the input is 0, such as a starting amount or a fixed fee. The order of the terms does not matter, so in 40 + 15h the 15 is still the rate of change. A minus sign in front of the rate means the amount goes down.
Try a similar one
The equation F = 3d + 8 gives the fare F, in dollars, for a taxi ride of d miles. What does the number 3 represent: the rate of change or the initial value?
✓ 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
💡 3 is the number multiplied by g, so it tells how much P changes for each 1 unit of g: each gigabyte adds 3 dollars to the bill. It is the rate of change.
✓ Correct!
Not quite. The answer is
💡 3 is the number multiplied by g, so it tells how much P changes for each 1 unit of g: each gigabyte adds 3 dollars to the bill. It is the rate of change.
💡 How to solve: Interpreting Rate of Change & Initial Value
In a linear model y = mx + b, the number multiplied by the input variable (m) is the rate of change: how much the output goes up or down for each 1 unit of the input. The number on its own (b) is the initial value: the output when the input is 0, such as a starting amount or a fixed fee. The order of the terms does not matter, so in 40 + 15h the 15 is still the rate of change. A minus sign in front of the rate means the amount goes down.
Try a similar one
The equation P = 3g + 36 gives the monthly phone bill P, in dollars, when g gigabytes of data are used. What does the number 3 represent: the rate of change or the initial value?
✓ 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
💡 253 is the number on its own, not multiplied by t. When t = 0, W = 253, so it is the water already in the pool, 253 liters. It is the initial value.
✓ Correct!
Not quite. The answer is
💡 253 is the number on its own, not multiplied by t. When t = 0, W = 253, so it is the water already in the pool, 253 liters. It is the initial value.
💡 How to solve: Interpreting Rate of Change & Initial Value
In a linear model y = mx + b, the number multiplied by the input variable (m) is the rate of change: how much the output goes up or down for each 1 unit of the input. The number on its own (b) is the initial value: the output when the input is 0, such as a starting amount or a fixed fee. The order of the terms does not matter, so in 40 + 15h the 15 is still the rate of change. A minus sign in front of the rate means the amount goes down.
Try a similar one
The equation W = 35t + 264 gives the water W, in liters, in a pool t minutes after a hose is turned on. What does the number 35 represent: the rate of change or the initial value?
✓ 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
💡 8 is the number on its own, not multiplied by d. When d = 0, F = 8, so it is the charge before the taxi moves, 8 dollars. It is the initial value.
✓ Correct!
Not quite. The answer is
💡 8 is the number on its own, not multiplied by d. When d = 0, F = 8, so it is the charge before the taxi moves, 8 dollars. It is the initial value.
💡 How to solve: Interpreting Rate of Change & Initial Value
In a linear model y = mx + b, the number multiplied by the input variable (m) is the rate of change: how much the output goes up or down for each 1 unit of the input. The number on its own (b) is the initial value: the output when the input is 0, such as a starting amount or a fixed fee. The order of the terms does not matter, so in 40 + 15h the 15 is still the rate of change. A minus sign in front of the rate means the amount goes down.
Try a similar one
The equation F = 3d + 4 gives the fare F, in dollars, for a taxi ride of d miles. What does the number 4 represent: the rate of change or the initial value?
✓ 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
💡 3 is the number multiplied by g, so it tells how much P changes for each 1 unit of g: each gigabyte adds 3 dollars to the bill. It is the rate of change.
✓ Correct!
Not quite. The answer is
💡 3 is the number multiplied by g, so it tells how much P changes for each 1 unit of g: each gigabyte adds 3 dollars to the bill. It is the rate of change.
💡 How to solve: Interpreting Rate of Change & Initial Value
In a linear model y = mx + b, the number multiplied by the input variable (m) is the rate of change: how much the output goes up or down for each 1 unit of the input. The number on its own (b) is the initial value: the output when the input is 0, such as a starting amount or a fixed fee. The order of the terms does not matter, so in 40 + 15h the 15 is still the rate of change. A minus sign in front of the rate means the amount goes down.
Try a similar one
The equation S = 5n + 83 gives the money S, in dollars, in Lena's savings account after n weeks. What does the number 5 represent: the rate of change or the initial value?
✓ 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
💡 148 is the number on its own, not multiplied by n. When n = 0, S = 148, so it is the money in the account at the start, 148 dollars. It is the initial value.
✓ Correct!
Not quite. The answer is
💡 148 is the number on its own, not multiplied by n. When n = 0, S = 148, so it is the money in the account at the start, 148 dollars. It is the initial value.
💡 How to solve: Interpreting Rate of Change & Initial Value
In a linear model y = mx + b, the number multiplied by the input variable (m) is the rate of change: how much the output goes up or down for each 1 unit of the input. The number on its own (b) is the initial value: the output when the input is 0, such as a starting amount or a fixed fee. The order of the terms does not matter, so in 40 + 15h the 15 is still the rate of change. A minus sign in front of the rate means the amount goes down.
Try a similar one
The equation F = 3d + 5 gives the fare F, in dollars, for a taxi ride of d miles. What does the number 5 represent: the rate of change or the initial value?
✓ 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
💡 10 is the number on its own, not multiplied by w. When w = 0, H = 10, so it is the plant's height when it was planted, 10 cm. It is the initial value.
✓ Correct!
Not quite. The answer is
💡 10 is the number on its own, not multiplied by w. When w = 0, H = 10, so it is the plant's height when it was planted, 10 cm. It is the initial value.
💡 How to solve: Interpreting Rate of Change & Initial Value
In a linear model y = mx + b, the number multiplied by the input variable (m) is the rate of change: how much the output goes up or down for each 1 unit of the input. The number on its own (b) is the initial value: the output when the input is 0, such as a starting amount or a fixed fee. The order of the terms does not matter, so in 40 + 15h the 15 is still the rate of change. A minus sign in front of the rate means the amount goes down.
Try a similar one
The equation C = 35h + 34 gives the cost C, in dollars, of renting a boat for h hours. What does the number 34 represent: the rate of change or the initial value?
✓ 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
💡 235 is the number on its own, not multiplied by t. When t = 0, W = 235, so it is the water already in the pool, 235 liters. It is the initial value.
✓ Correct!
Not quite. The answer is
💡 235 is the number on its own, not multiplied by t. When t = 0, W = 235, so it is the water already in the pool, 235 liters. It is the initial value.
💡 How to solve: Interpreting Rate of Change & Initial Value
In a linear model y = mx + b, the number multiplied by the input variable (m) is the rate of change: how much the output goes up or down for each 1 unit of the input. The number on its own (b) is the initial value: the output when the input is 0, such as a starting amount or a fixed fee. The order of the terms does not matter, so in 40 + 15h the 15 is still the rate of change. A minus sign in front of the rate means the amount goes down.
Try a similar one
The equation C = 32h + 49 gives the cost C, in dollars, of renting a boat for h hours. What does the number 32 represent: the rate of change or the initial value?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Interpreting Rate of Change & Initial Value — Easy Worksheet 2
Answer each question with "rate of change" or "initial value".