A hot cup of coffee is left on a table to cool. The temperature of the coffee decreases by 3°F every minute. The coffee started at 150°F.

Which equation can be used to find y the coffee's temperature after x minutes?

The problem describes a situation where the coffee's temperature decreases by 3°F every minute, starting from an initial temperature of 150°F. This suggests a linear relationship between time and temperature.

The general form for a linear equation is:

\[
y = mx + b
\]

Where:
- \( y \) is the coffee's temperature after \( x \) minutes.
- \( m \) is the slope (rate of change), which represents how much the temperature changes per minute.
- \( b \) is the y-intercept, which is the starting temperature at time \( x = 0 \).

Given:
- The temperature decreases by 3°F per minute, so \( m = -3 \).
- The initial temperature (at \( x = 0 \)) is 150°F, so \( b = 150 \).

Thus, the equation becomes:

\[
y = -3x + 150
\]

This equation can be used to find \( y \), the coffee's temperature after \( x \) minutes.

---

Would you like more details or have any questions? Here are 5 related questions to deepen your understanding:

1. What is the temperature of the coffee after 10 minutes?
2. After how many minutes will the coffee reach a temperature of 100°F?
3. How would the equation change if the coffee cooled faster, at 5°F per minute?
4. Can you rewrite the equation if the coffee started at 180°F instead of 150°F?
5. What happens to the temperature graph after 50 minutes?

**Tip:** In linear equations, the slope \( m \) always represents the rate of change, which helps predict how much a quantity increases or decreases over time.

A hot cup of coffee is left on a table to cool. The temperature of the coffee decreases by 3°F every minute. The coffee started at 150°F. Which equation can be used to find y, the coffee's temperature after x minutes?

Discover how to use a linear equation to model the cooling of a hot cup of coffee. Learn how to apply the slope-intercept formula to find the coffee's temperature over time, suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation