Ryan starts saving money to buy a car right after his 16th birthday. He already has $120 from his birthday. After 3 months he has $840 altogether. After 10 months he has $2520 altogether. Find the linear equation that models the data. Using your equation, find how much money Ryan will have altogether after saving for 2 years?

Remark

The basic equation is y = mx + b

y = the total amount of money

m = The amount of money he save each month (it is a constant).

b = the y intercept which is his starting amount or 120 dollars.

x = the number of months (this is a variable).

After 3 months he has 840 dollars. That's y

840 = 3*m + 120 Subtract 120 from both sides

840 - 120 = 3m

720 = 3m

240 = m So he saves 240 every month.

Now the equation becomes.

y = 240 * x + 120

Savings after 24 months

y = Total

m = 240 dollars/month

x = 24 months

b = 120

y = 24*240 + 120

y = 5760 + 120

y = 5580

He had 5580 dollars after saving for 2 years (or 24 months total) This assumes that when he started, he took his birthday money and added a 1 month payment to it