In the function [tex]\( r(v) = 12 - 3v \)[/tex], we need to determine which variable is the dependent variable.
A dependent variable is a variable that depends on one or more other variables. It changes in response to the value of other variables. In this function, let's identify the variables and their roles:
- [tex]\( v \)[/tex] is the independent variable. This means [tex]\( v \)[/tex] can take any value and is not dependent on other variables in this equation.
- [tex]\( r \)[/tex] is the dependent variable. This means [tex]\( r \)[/tex] depends on the value of [tex]\( v \)[/tex]. As [tex]\( v \)[/tex] changes, [tex]\( r \)[/tex] will change according to the equation.
Let's see how [tex]\( r \)[/tex] changes with different values of [tex]\( v \)[/tex]:
- If [tex]\( v = 0 \)[/tex]:
[tex]\[
r(0) = 12 - 3 \cdot 0 = 12
\][/tex]
- If [tex]\( v = 1 \)[/tex]:
[tex]\[
r(1) = 12 - 3 \cdot 1 = 12 - 3 = 9
\][/tex]
- If [tex]\( v = 2 \)[/tex]:
[tex]\[
r(2) = 12 - 3 \cdot 2 = 12 - 6 = 6
\][/tex]
From these examples, you can see that [tex]\( r \)[/tex] changes based on the value of [tex]\( v \)[/tex].
Therefore, the dependent variable in the function [tex]\( r(v) = 12 - 3v \)[/tex] is [tex]\( \boxed{r} \)[/tex].
