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Question 6 of 11

The temperature in Minsk was recorded over a period of four hours. The equation

[tex]\[ y = -5x + 54 \][/tex]

describes the temperature over this time, where [tex]\( y \)[/tex] is the temperature in degrees Fahrenheit ([tex]\(^{\circ}F\)[/tex]) and [tex]\( x \)[/tex] is the number of hours since measurements started. Which of the following statements correctly describes the temperature?

A. It was [tex]\( 54^{\circ} F \)[/tex] when the temperature was first measured, and it is dropping by 5 degrees per hour.

B. It was [tex]\( -5^{\circ} F \)[/tex] after four hours, and it is rising by 54 degrees per hour.

C. It was [tex]\( -5^{\circ} F \)[/tex] when the temperature was first measured, and it is rising by 54 degrees per hour.

D. It was [tex]\( 54^{\circ} F \)[/tex] after four hours, and it is dropping by 5 degrees per hour.

Sagot :

GinnyAnswer
To answer this question, we need to analyze the given linear equation:
[tex]\[ y = -5x + 54 \][/tex]

This equation describes the temperature [tex]\( y \)[/tex] in degrees Fahrenheit (°F) as a function of [tex]\( x \)[/tex], the number of hours since measurements started.

### Step-by-Step Solution:

1. Initial Temperature:
- When the temperature was first measured, [tex]\( x = 0 \)[/tex].
- Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = -5(0) + 54 \][/tex]
[tex]\[ y = 54 \][/tex]
- Therefore, the initial temperature (when [tex]\( x = 0 \)[/tex]) was [tex]\( 54 \)[/tex]°F.

2. Rate of Change:
- The coefficient of [tex]\( x \)[/tex] in the equation [tex]\( y = -5x + 54 \)[/tex] is [tex]\(-5\)[/tex].
- This coefficient represents the rate of change of temperature per hour.
- A negative coefficient ([tex]\(-5\)[/tex]) indicates that the temperature is dropping.
- Thus, the temperature is dropping by 5 degrees per hour.

3. Correct Statement:
- Based on the initial temperature and the rate of change:
- It was [tex]\( 54 \)[/tex]°F when the temperature was first measured (when [tex]\( x = 0 \)[/tex]).
- The temperature is dropping by 5 degrees per hour.

### Conclusion:
The statement that correctly describes the temperature is:
A. It was [tex]\( 54^{\circ} F \)[/tex] when the temperature was first measured, and it is dropping by 5 degrees per hour.
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