Question

How can linear functions be used to model situations and solve problems?

Answer 1

One day, you go to a store and buy a pencil. It costs $0.25.
You notice the unit price $0.25/pencil.

The next day you buy 3 pencils, they cost $0.75.
You notice the unit price is $0.75/(3 pencils) = $0.25/pencil.

For each extra pencil you buy, the increase in price is always $0.25.
This suggests a linear relation between the number of pencils, p, and the cost of the pencils, c.

You use a linear equation to give you the cost of pencils based on the number of pencils.

c = 0.25p

One day, you happen to have $4.50 in your pocket.
You'd like to buy 15 pencils, but you are not sure you have enough money.
You use your handy linear equation, and you replace p, the number of pencils, with 15 to find their cost, c.

c = 0.25p

c = 0.25 * 15

c = 3.75

After using your equation, you see that 15 pencils cost $3.75, and since you have $4.50 you have enough money to buy them. You're very happy about this, and, as soon as you get home, you write this experience in your journal, using one of the new pencils you just bought, and you make it a point to include the linear equation that helped you.