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Writing a Linear Function from a Word Problem — Easy Worksheet 2
Grade 8 · Whoobee Name: ____________________ Date: __________
Write an equation in the form y = mx + b for each situation.
How to solve
The initial value b is the starting amount or fixed fee, the value of y when x = 0. The rate of change m is how much y changes for each 1 unit of x; it is negative when the amount goes down. When you are given two data points instead, m = (change in y) ÷ (change in x), and you find b by working back to x = 0. Then write y = mx + b.
Example
A sunflower is 22 cm tall and grows 3 cm every week. Write an equation for y, the height of the sunflower in cm, after x weeks.
Answer: y = 3x + 22
Not quite. The answer is
💡 The starting amount (when x = 0) is 80, so b = 80. It goes up by 20 each week, so m = 20. So y = 20x + 80.
✓ Correct!
Not quite. The answer is
💡 The starting amount (when x = 0) is 80, so b = 80. It goes up by 20 each week, so m = 20. So y = 20x + 80.
💡 How to solve: Writing a Linear Function from a Word Problem
The initial value b is the starting amount or fixed fee, the value of y when x = 0. The rate of change m is how much y changes for each 1 unit of x; it is negative when the amount goes down. When you are given two data points instead, m = (change in y) ÷ (change in x), and you find b by working back to x = 0. Then write y = mx + b.
Try a similar one
Sam has $138 saved and adds $5 every week. Write an equation for y, the amount saved in dollars, after x weeks.
✓ 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 60, so b = 60. It goes up by 54 each hour, so m = 54. So y = 54x + 60.
✓ Correct!
Not quite. The answer is
💡 The starting amount (when x = 0) is 60, so b = 60. It goes up by 54 each hour, so m = 54. So y = 54x + 60.
💡 How to solve: Writing a Linear Function from a Word Problem
The initial value b is the starting amount or fixed fee, the value of y when x = 0. The rate of change m is how much y changes for each 1 unit of x; it is negative when the amount goes down. When you are given two data points instead, m = (change in y) ÷ (change in x), and you find b by working back to x = 0. Then write y = mx + b.
Try a similar one
Sam has $98 saved and adds $19 every week. Write an equation for y, the amount saved in dollars, after x weeks.
✓ 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 5, so b = 5. It goes up by 3 each mile, so m = 3. So y = 3x + 5.
✓ Correct!
Not quite. The answer is
💡 The starting amount (when x = 0) is 5, so b = 5. It goes up by 3 each mile, so m = 3. So y = 3x + 5.
💡 How to solve: Writing a Linear Function from a Word Problem
The initial value b is the starting amount or fixed fee, the value of y when x = 0. The rate of change m is how much y changes for each 1 unit of x; it is negative when the amount goes down. When you are given two data points instead, m = (change in y) ÷ (change in x), and you find b by working back to x = 0. Then write y = mx + b.
Try a similar one
A gym charges a $86 sign-up fee plus $16 per month. Write an equation for y, the total cost in dollars, after x months.
✓ 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 68, so b = 68. It goes up by 44 each month, so m = 44. So y = 44x + 68.
✓ Correct!
Not quite. The answer is
💡 The starting amount (when x = 0) is 68, so b = 68. It goes up by 44 each month, so m = 44. So y = 44x + 68.
💡 How to solve: Writing a Linear Function from a Word Problem
The initial value b is the starting amount or fixed fee, the value of y when x = 0. The rate of change m is how much y changes for each 1 unit of x; it is negative when the amount goes down. When you are given two data points instead, m = (change in y) ÷ (change in x), and you find b by working back to x = 0. Then write y = mx + b.
Try a similar one
A sunflower is 39 cm tall and grows 9 cm every week. Write an equation for y, the height of the sunflower in cm, after x weeks.
✓ 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 86, so b = 86. It goes up by 38 each hour, so m = 38. So y = 38x + 86.
✓ Correct!
Not quite. The answer is
💡 The starting amount (when x = 0) is 86, so b = 86. It goes up by 38 each hour, so m = 38. So y = 38x + 86.
💡 How to solve: Writing a Linear Function from a Word Problem
The initial value b is the starting amount or fixed fee, the value of y when x = 0. The rate of change m is how much y changes for each 1 unit of x; it is negative when the amount goes down. When you are given two data points instead, m = (change in y) ÷ (change in x), and you find b by working back to x = 0. Then write y = mx + b.
Try a similar one
A sunflower is 18 cm tall and grows 9 cm every week. Write an equation for y, the height of the sunflower in cm, after x weeks.
✓ 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 79, so b = 79. It goes up by 18 each week, so m = 18. So y = 18x + 79.
✓ Correct!
Not quite. The answer is
💡 The starting amount (when x = 0) is 79, so b = 79. It goes up by 18 each week, so m = 18. So y = 18x + 79.
💡 How to solve: Writing a Linear Function from a Word Problem
The initial value b is the starting amount or fixed fee, the value of y when x = 0. The rate of change m is how much y changes for each 1 unit of x; it is negative when the amount goes down. When you are given two data points instead, m = (change in y) ÷ (change in x), and you find b by working back to x = 0. Then write y = mx + b.
Try a similar one
A taxi ride costs $4 plus $4 per mile. Write an equation for y, the fare in dollars, after x miles.
✓ 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 6, so b = 6. It goes up by 3 each mile, so m = 3. So y = 3x + 6.
✓ Correct!
Not quite. The answer is
💡 The starting amount (when x = 0) is 6, so b = 6. It goes up by 3 each mile, so m = 3. So y = 3x + 6.
💡 How to solve: Writing a Linear Function from a Word Problem
The initial value b is the starting amount or fixed fee, the value of y when x = 0. The rate of change m is how much y changes for each 1 unit of x; it is negative when the amount goes down. When you are given two data points instead, m = (change in y) ÷ (change in x), and you find b by working back to x = 0. Then write y = mx + b.
Try a similar one
A pool holds 208 liters of water, and a hose adds 13 liters every minute. Write an equation for y, the water in the pool in liters, after x minutes.
✓ 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 41, so b = 41. It goes up by 22 each month, so m = 22. So y = 22x + 41.
✓ Correct!
Not quite. The answer is
💡 The starting amount (when x = 0) is 41, so b = 41. It goes up by 22 each month, so m = 22. So y = 22x + 41.
💡 How to solve: Writing a Linear Function from a Word Problem
The initial value b is the starting amount or fixed fee, the value of y when x = 0. The rate of change m is how much y changes for each 1 unit of x; it is negative when the amount goes down. When you are given two data points instead, m = (change in y) ÷ (change in x), and you find b by working back to x = 0. Then write y = mx + b.
Try a similar one
A taxi ride costs $8 plus $2 per mile. Write an equation for y, the fare in dollars, after x miles.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Writing a Linear Function from a Word Problem — Easy Worksheet 2
Write an equation in the form y = mx + b for each situation.