At the end of the day, a pizzeria turns off its pizza oven. The table shows the linear relationship between the temperature, y, of the oven x minutes after turning it off.

Question

MIn:0,1,2,3,4,
temp:425,400,375,350,325

What is the slope and what does it represent in this situation?

Answer 1

To find the slope of the linear relationship described in your data, we can use the formula for the slope \( m \) of a line given two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Let's look at two points from your data:

• At \( x = 0 \) minutes, \( y = 425 \) degrees.
• At \( x = 4 \) minutes, \( y = 325 \) degrees.

Using these points, we can calculate the slope:

\[ m = \frac{325 - 425}{4 - 0} = \frac{-100}{4} = -25 \]

So, the slope \( m \) is \(-25\).

Interpretation of the Slope

The slope of \(-25\) means that for each minute after the oven is turned off, the temperature of the oven decreases by \(25\) degrees Fahrenheit. This indicates a consistent rate at which the oven cools down over time.