What you’ll learn
Model real situations with linear functions.
Key idea
A linear cost model adds a fixed starting amount to rate multiplied by the number of elapsed units.
Rate multiplies elapsed months; fixed fee contributes once, including at zero months.
Worked example
Enter the exact value or ordered values in the format requested below.
A club charges a one-time $18 fee plus $2 per month; x is nonnegative whole months and y total dollars. Write the linear equation relating y and x.
- At zero months, the one-time fee contributes $18; every month contributes $2.
- With x nonnegative whole months and y dollars, total is y=2x+18. Rate 2 multiplies x; fixed fee 18 does not.
Answer: y=2x+18
Quick Check
Choose which candidate representation satisfies the requirements of 'Model real situations with linear functions' and justify the choice.
A club charges a one-time $7 fee plus $4 per month; x is nonnegative whole months and y total dollars. Select the model and justify both terms.