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

This problem involves a linear relationship between the time (in minutes) and the temperature of the coffee. The key points are:

- The coffee's initial temperature is 150°F.
- The temperature decreases by 3°F per minute.

This means that the rate of change in temperature is \(-3\) (since it cools, not heats). The initial temperature of the coffee is 150°F, which will act as the y-intercept in the equation. 

The general equation of a line is:
\[
y = mx + b
\]
Where:
- \(m\) is the slope (rate of change, in this case, \(-3\)).
- \(b\) is the y-intercept (initial temperature, 150°F).

Thus, the equation is:
\[
y = -3x + 150
\]
This matches option **D**.

### Answer: D. \( y = -3x + 150 \)

Would you like any further details or have any questions?

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Here are 5 questions related to this problem:
1. What is the coffee's temperature after 5 minutes?
2. How long does it take for the coffee to cool to 100°F?
3. How would the equation change if the coffee cooled by 4°F every minute instead of 3°F?
4. What does the slope of the equation represent in this context?
5. How would the equation look if the initial temperature were 180°F?

**Tip:** Linear equations are perfect for representing situations with constant rates of change.

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? Options: A. y=3x−150, B. y=3x+150, C. y=−3x−150, D. y=−3x+150

Solve the problem of a cooling cup of coffee with a temperature that decreases by 3°F per minute, starting at 150°F. Learn how to form and use the linear equation y = -3x + 150 to find the coffee's temperature after x minutes. Suitable for Grades 6-8 students learning linear equations.

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