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?
A.y=3x−150

B.y=3x+150

C.y=−3x−150

D.y=−3x+150


The problem describes a situation where the temperature of the coffee is decreasing by 3°F every minute, starting at 150°F. This can be modeled by a linear equation, where:

- \( y \) is the coffee's temperature after \( x \) minutes.
- The rate of change is \(-3\) (since the temperature decreases by 3°F per minute).
- The initial temperature (when \( x = 0 \)) is 150°F.

Thus, the equation will have the form:
\[
y = -3x + 150
\]

This is because:
- \( -3x \) represents the decrease in temperature over time.
- \( 150 \) is the initial temperature when no time has passed.

So, the correct equation is:

**D. \( y = -3x + 150 \)**

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How would the equation change if the coffee cooled faster, say 5°F per minute?
2. What would be the coffee's temperature after 10 minutes using this equation?
3. How can you modify the equation if the starting temperature was different?
4. Can this type of equation be used for heating a substance instead of cooling? How?
5. How long will it take for the coffee to cool to 100°F?

**Tip**: In linear equations, the slope represents the rate of change, and the y-intercept represents the initial condition.

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? A. y = 3x - 150, B. y = 3x + 150, C. y = -3x - 150, D. y = -3x + 150

Explore how to model the cooling of a hot cup of coffee using a linear equation. This problem demonstrates the key concept of linear equations with a cooling rate of 3°F per minute, starting at 150°F. Suitable for students in Grades 6-8.

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