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Interpreting Rate of Change & Initial Value — Easy Worksheet 1
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
💡 74 is the number on its own, not multiplied by h. When h = 0, C = 74, so it is the fee you pay before any hours, 74 dollars. It is the initial value.
✓ Correct!
Not quite. The answer is
💡 74 is the number on its own, not multiplied by h. When h = 0, C = 74, so it is the fee you pay before any hours, 74 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 = 2d + 4 gives the fare F, in dollars, for a taxi ride of d miles. What does the number 2 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 multiplied by n, so it tells how much S changes for each 1 unit of n: she adds 8 dollars each week. It is the rate of change.
✓ Correct!
Not quite. The answer is
💡 8 is the number multiplied by n, so it tells how much S changes for each 1 unit of n: she adds 8 dollars each week. 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 H = 3w + 5 gives the height H, in centimeters, of a plant w weeks after it was planted. 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
💡 11 is the number on its own, not multiplied by w. When w = 0, H = 11, so it is the plant's height when it was planted, 11 cm. It is the initial value.
✓ Correct!
Not quite. The answer is
💡 11 is the number on its own, not multiplied by w. When w = 0, H = 11, so it is the plant's height when it was planted, 11 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 = 12h + 26 gives the cost C, in dollars, of renting a boat for h hours. What does the number 26 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
💡 179 is the number on its own, not multiplied by n. When n = 0, S = 179, so it is the money in the account at the start, 179 dollars. It is the initial value.
✓ Correct!
Not quite. The answer is
💡 179 is the number on its own, not multiplied by n. When n = 0, S = 179, so it is the money in the account at the start, 179 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 + 6 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
💡 2 is the number multiplied by d, so it tells how much F changes for each 1 unit of d: the fare goes up by 2 dollars for each mile. It is the rate of change.
✓ Correct!
Not quite. The answer is
💡 2 is the number multiplied by d, so it tells how much F changes for each 1 unit of d: the fare goes up by 2 dollars for each mile. 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 C = 13h + 38 gives the cost C, in dollars, of renting a boat for h hours. What does the number 38 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
💡 32 is the number on its own, not multiplied by g. When g = 0, P = 32, so it is the bill before any data is used, 32 dollars. It is the initial value.
✓ Correct!
Not quite. The answer is
💡 32 is the number on its own, not multiplied by g. When g = 0, P = 32, so it is the bill before any data is used, 32 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 = 2d + 7 gives the fare F, in dollars, for a taxi ride of d miles. What does the number 7 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
💡 5 is the number on its own, not multiplied by w. When w = 0, H = 5, so it is the plant's height when it was planted, 5 cm. It is the initial value.
✓ Correct!
Not quite. The answer is
💡 5 is the number on its own, not multiplied by w. When w = 0, H = 5, so it is the plant's height when it was planted, 5 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 H = 4w + 13 gives the height H, in centimeters, of a plant w weeks after it was planted. What does the number 13 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
💡 29 is the number multiplied by h, so it tells how much C changes for each 1 unit of h: the cost goes up by 29 dollars for each hour. It is the rate of change.
✓ Correct!
Not quite. The answer is
💡 29 is the number multiplied by h, so it tells how much C changes for each 1 unit of h: the cost goes up by 29 dollars for each hour. 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 H = 5w + 7 gives the height H, in centimeters, of a plant w weeks after it was planted. What does the number 7 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 1
Answer each question with "rate of change" or "initial value".