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 coffee's temperature decreases by 3°F every minute. This means that the rate of change in temperature is -3°F per minute. The coffee starts at 150°F, so the initial temperature is 150°F.

The general form of the equation for this linear relationship is:

\[
y = \text{{rate of change}} \times x + \text{{initial value}}
\]

Where:
- \( y \) is the coffee's temperature after \( x \) minutes,
- \( x \) is the time in minutes,
- The rate of change is \(-3\)°F per minute (since the temperature is decreasing),
- The initial temperature is 150°F.

Thus, the equation becomes:

\[
y = -3x + 150
\]

So, the correct answer is:

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

Would you like any further details or explanations?

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Here are 5 related questions to expand on this:
1. How would the equation change if the coffee cooled at a different rate?
2. What does the slope of the equation represent in this context?
3. After how many minutes will the coffee reach room temperature if the room is 70°F?
4. How would the equation change if the coffee started at a different initial temperature?
5. Can you graph this equation and describe its characteristics?

**Tip:** Linear equations like this one have constant rates of change, making them ideal for modeling situations like temperature cooling or heating.

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

Discover how to model the cooling of a hot cup of coffee using a linear equation. The temperature decreases by 3°F per minute, starting at 150°F. Learn how to form the equation y = -3x + 150, ideal for students in Grades 6-8.

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