Let's carefully analyze the given equation [tex]\( y = 45x + 67 \)[/tex].
In this equation:
- [tex]\( y \)[/tex] represents the final temperature of the oven in degrees Fahrenheit.
- [tex]\( x \)[/tex] represents the number of minutes.
- The coefficient 45 is multiplied by [tex]\( x \)[/tex], which indicates the rate of temperature increase per minute.
- The number 67 is added as a constant term.
The key question is to interpret what the constant term (67) represents.
Here are the options provided:
1. The change in minutes for every change of one degree Fahrenheit.
2. The change in degrees Fahrenheit for every change of one minute.
3. The temperature the oven starts at.
4. The time when the oven's temperature is [tex]\( 0^\circ \)[/tex]F.
Now, let's analyze each option:
1. The change in minutes for every change of one degree Fahrenheit: This option implies a relationship in the units of minutes per degree, which doesn't match the role of a constant term in a linear equation.
2. The change in degrees Fahrenheit for every change of one minute: This option corresponds to a rate of change, which is represented by the coefficient 45 rather than the constant 67.
3. The temperature the oven starts at: In the context of the equation, this option seems appropriate. When [tex]\( x = 0 \)[/tex], the equation simplifies to [tex]\( y = 67 \)[/tex]. This means initially, when no time has elapsed (at [tex]\( x = 0 \)[/tex]), the oven's temperature is 67 degrees Fahrenheit.
4. The time when the oven's temperature is [tex]\( 0^\circ \)[/tex]F: This implies solving for [tex]\( x \)[/tex] when [tex]\( y = 0 \)[/tex], which again does not align with the role of 67 in the equation.
Given this detailed analysis, it's clear that the constant term 67 represents the temperature the oven starts at.
Therefore, the number 67 in Tamika's equation represents "the temperature the oven starts at."
