Question

question
tamika is preheating her oven before using it to bake. tamika wants to predict the final temperature after x minutes. she wrote the equation y = 45x + 67, where y represents the final temperature in degrees fahrenheit. what could the number 67 in tamika’s equation represent?
answer
the change in minutes for every change of one degree fahrenheit.
the temperature the oven starts at.
the change in degrees fahrenheit for every change of one minute.
the time when the oven’s temperature is 0°.

Explanation:

Step1: Recall slope-intercept form

The equation of a line in slope - intercept form is \(y = mx + b\), where \(m\) is the slope (rate of change) and \(b\) is the y - intercept (initial value when \(x = 0\)).

Step2: Analyze the given equation

In the equation \(y=45x + 67\), \(x\) represents the number of minutes and \(y\) represents the temperature in degrees Fahrenheit. When \(x = 0\) (at the start, when no minutes have passed), \(y=67\). So the value 67 represents the initial temperature of the oven, i.e., the temperature the oven starts at.
Let's analyze the other options:

• The change in minutes for every change of one degree Fahrenheit: The slope \(m = 45\) represents the change in \(y\) (temperature) per change in \(x\) (minutes), not the other way around. So this is incorrect.
• The change in degrees Fahrenheit for every change of one minute: This is the slope (\(m = 45\)), not 67. So this is incorrect.
• The time when the oven’s temperature is \(0^{\circ}\): To find when \(y = 0\), we solve \(0=45x + 67\), \(x=-\frac{67}{45}\), which is not 67. So this is incorrect.

Answer:

The temperature the oven starts at.