Writing linear equations from a context
A linear model has a starting value (the output when the input is 0) and a rate (how much the output changes for each 1 unit of input). Find both, with their units, and write y = mx + b.
Work in the notepad at the bottom of the screen. Write the way you would on paper. When you pause, a typed copy of what you wrote appears beside it: tap the copy to fix it, and use the graph button on any formula to see it.
1. Bike rental
A bike rental shop charges a $12 fee plus $4 for every hour. Write an equation for the cost C, in dollars, of renting a bike for h hours.
Check your equation: what does it give for a 3-hour rental?
2. A draining tank
A tank holds 60 gallons of water. It drains at 3 gallons per minute. Write an equation for the water W, in gallons, left in the tank after t minutes.
For which values of t does your model make sense?
3. The plumber's bill
A plumber charges a call-out fee plus a fixed rate per hour. A 3-hour job costs $185. A 5-hour job costs $265.
- Find the hourly rate.
- Find the call-out fee.
- Write an equation for the cost C of an h-hour job, and check it with both jobs.
4. A gift card
Mia spends the same amount from a gift card every day. The table shows the balance B, in dollars, after d days.
| Days, d | 2 | 4 | 7 |
|---|---|---|---|
| Balance, B ($) | 84 | 68 | 44 |
Write an equation for B in terms of d. How much was on the card at the start?
Careful: the first column of the table is not day 0.
5. Two phone plans
Plan A costs $25 a month plus $0.10 per text. Plan B costs $15 a month plus $0.20 per text. Write an equation for the monthly cost y of each plan for x texts.
Open the graph of one plan and add the other plan to it. Where do the lines cross, and what does that point mean for someone choosing a plan?