# Soda is on sale for $0.75 a can, and you have a coupon for$0.50 off your total purchase. How do you write a function rule for the cost of n sodas. How much would 10 sodas cost?

Jan 7, 2017

$c = 0.75 n - 0.5$ where $c$ is your total cost in dollars and $n$ is the number of sodas bought.

$10$ sodas would cost $7.00. #### Explanation: We can start with a single formula $y = M x + b$. This is used in the case of only one variable being changed at a constant rate (e.g. a cost per item). $M$is your "cost per" (or slope, but in the cases of buying and selling, it means the same). Since a soda costs $0.75, $M$ can be replaced with $0.75$.

With this information, we can say,
$y = 0.75 x + b$

$b$ is your "base value" (it may also be referred to as a $y$-intercept). In this situation, it is not too easy to define a base value because it isn't really a base value, it's just a single change in the total outcome. Your base value is from your coupon, which takes away $0.50 from the total cost of the purchase. Since the $0.50 is taken away, $b$ is $- 0.50$. When $b$ is a negative, you can subtract the value rather than add.

So now we get,
$y = 0.75 x - 0.5$

As for the $x$ and the $y$. The $y$ is the outcome of the change in the $x$, and the $x$ is typically what can easily be changed in the given problem. So, $x$ is the number of sodas ($n$) and $y$ is the total cost ($c$).

So we end up with,
$c = 0.75 n - 0.5$ where $c$ is your total cost in dollars and $n$ is the number of sodas bought.

Sorry if this is a bit lengthy, but I hope it helped. Cheers, and best of luck to you!