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Writing a Linear Function from a Word Problem — Easy Worksheet 1
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 150, so b = 150. It goes up by 37 each minute, so m = 37. So y = 37x + 150.
✓ Correct!
Not quite. The answer is
💡 The starting amount (when x = 0) is 150, so b = 150. It goes up by 37 each minute, so m = 37. So y = 37x + 150.
💡 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 $38 sign-up fee plus $13 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 58, so b = 58. It goes up by 40 each month, so m = 40. So y = 40x + 58.
✓ Correct!
Not quite. The answer is
💡 The starting amount (when x = 0) is 58, so b = 58. It goes up by 40 each month, so m = 40. So y = 40x + 58.
💡 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 $31 sign-up fee plus $25 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 69, so b = 69. It goes up by 45 each hour, so m = 45. So y = 45x + 69.
✓ Correct!
Not quite. The answer is
💡 The starting amount (when x = 0) is 69, so b = 69. It goes up by 45 each hour, so m = 45. So y = 45x + 69.
💡 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 13 cm tall and grows 4 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 4, so b = 4. It goes up by 2 each mile, so m = 2. So y = 2x + 4.
✓ Correct!
Not quite. The answer is
💡 The starting amount (when x = 0) is 4, so b = 4. It goes up by 2 each mile, so m = 2. So y = 2x + 4.
💡 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 $83 sign-up fee plus $27 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 131, so b = 131. It goes up by 14 each week, so m = 14. So y = 14x + 131.
✓ Correct!
Not quite. The answer is
💡 The starting amount (when x = 0) is 131, so b = 131. It goes up by 14 each week, so m = 14. So y = 14x + 131.
💡 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 $58 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 168, so b = 168. It goes up by 17 each minute, so m = 17. So y = 17x + 168.
✓ Correct!
Not quite. The answer is
💡 The starting amount (when x = 0) is 168, so b = 168. It goes up by 17 each minute, so m = 17. So y = 17x + 168.
💡 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 $5 plus $5 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 4, so b = 4. It goes up by 5 each mile, so m = 5. So y = 5x + 4.
✓ Correct!
Not quite. The answer is
💡 The starting amount (when x = 0) is 4, so b = 4. It goes up by 5 each mile, so m = 5. So y = 5x + 4.
💡 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 plumber charges $75 for a visit plus $53 per hour. Write an equation for y, the charge in dollars, after x hours.
✓ 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 23, so b = 23. It goes up by 4 each week, so m = 4. So y = 4x + 23.
✓ Correct!
Not quite. The answer is
💡 The starting amount (when x = 0) is 23, so b = 23. It goes up by 4 each week, so m = 4. So y = 4x + 23.
💡 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 $71 sign-up fee plus $29 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.
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Writing a Linear Function from a Word Problem — Easy Worksheet 1
Write an equation in the form y = mx + b for each situation.