To identify the independent and dependent variables in the function [tex]\( t = 19m + 65 \)[/tex], let's break down what the function represents and how these variables interact.
1. Understanding the Function:
- The function [tex]\( t = 19m + 65 \)[/tex] tells us that the temperature [tex]\( t \)[/tex] in degrees Fahrenheit of the oven is determined by how many minutes [tex]\( m \)[/tex] it has been preheating.
- Here, [tex]\( t \)[/tex] (temperature) is expressed in terms of [tex]\( m \)[/tex] (minutes).
2. Independent Variable:
- The independent variable is the one that you manipulate or control.
- In this scenario, the time [tex]\( m \)[/tex] (in minutes) is the variable you can control. You decide how long the oven preheats.
3. Dependent Variable:
- The dependent variable is the one that responds to the changes in the independent variable.
- Here, the temperature [tex]\( t \)[/tex] (in degrees Fahrenheit) depends on how many minutes [tex]\( m \)[/tex] you have been preheating the oven. The temperature changes as time passes.
4. Identifying the Variables:
- Independent Variable: [tex]\( m \)[/tex] (minutes)
- Dependent Variable: [tex]\( t \)[/tex] (temperature in degrees Fahrenheit)
So, the independent variable is [tex]\( m \)[/tex] (minutes), and the dependent variable is [tex]\( t \)[/tex] (temperature in degrees Fahrenheit).
