A linear model fits savings that grow by the same amount each week. Multiply the weekly savings by the number of weeks, then add the money already saved. Use a one-variable regression in Desmos to match that total to the goal. The starting savings are added once, not once per week.
Hints
- Hint 1
A rate in dollars per week becomes a total in dollars when you multiply by the number of weeks. Only the new savings repeat. What expression gives all the money Laura adds in weeks?
- Hint 2
A starting amount is money Laura has before making any weekly deposits. Add it once to her new savings. What equation makes that sum equal the bicycle’s price?
Step-by-step
Build the savings equation and solve
Step 1Write the new savings
Let be the dollars Laura saves per week. She saves the same amount each week, so in weeks she adds dollars. The multiplies the weekly amount, not the money she already has.
- Step 2
Make the total equal the goal
Laura starts with $85, and the bicycle costs $260, so her starting money plus her new savings must equal the price: . The $85 is added only once because she already has it.
- Step 3
Find the weekly amount
Type in Desmos. The subscript in makes it a value Desmos can find, and tells Desmos to match the two sides. Under PARAMETERS, it shows . Since means dollars per week, Laura needs to save $25 each week. Grid in 25.